1.d4 d5 2.c4... Which system for Black is more solid/strategic?
I always tell all advocates of the French Defense to take up the King's Indian Defense.
The French is considered the second most aggressive defense to 1.e4, behind only the Sicilian. The major difference is the pawn chains blocking the diagonal that the King normally resides on (a2-g8) and hence a safer King in most cases.
That said, the blocked nature of the center, where the pawn pointing theory comes into play, where White attacks Kingside because that's the direction his pawns point (those that are amongst the blocked center that) and Black's pawns point Queenside and hence Black attacks the Queenside.
Take a look at the King's Indian Defense. Exact same thing! The center is completely blocked with pawns, and each side attacks in the direction in which the blocked pawns point. Black in this case the Kingside, White the Queenside!
From what I usually see, French players generally premove ...e6 (hoping to transpose to their favorite opening after 1.d4 e6 2,e4) to anything so they play Nimzo-Indian, or Dutch with ...e6.
but KID makes sense too, Petrosian regularly employed KID and French in his games maybe you should go look at that for reference.
The 1 d4 cousin to the French is the Queen's Gambit Declined, both playing d5 and e6 - which blocks in the Black QB but allows a later ...c5 in one move if you counterattack Q-side.
Personally I like the Slav and Caro-Kann (...c6 instead of ...e6) because it allows the Black QB to move to f5 or g4 before it gets blocked-in by e6 or else White must open up the game a little - with Black's equalization to keep the B off the K-side.
As mentioned above that means two moves are needed to post a pawn on c5 instead of one, but still prefer it.
I often respond to 1 e4, 1 d4, or 1 c4 with ...c6: it generally transposed to the Slav or Caro.
After 1. d4 d5 you will get the french very rarely. White cannot force that, with black you'll have the choice to go another way with at least equal good chances, e. g. by accapting the BDG after 1. d4 d5 2. e4 dxe4 instead of the french 2... e6. After 1. d4 d5 2. c4 e6 or 2. Nf3 Nf6 there is no serious way into the french. So you have the free choice on move two.
Therefore i would concider the classical slav 1. d4 d5 2. c4 c6 3. Nf3 Nf6 4. Nc3 dxc4 followed by Bc5.
Check out this article: http://chesswinning.com/10-best-chess-openings/
I play the French against 1.e4 and I like the Slav in response to the Queens Gambit, the Slav can be very strategic.
There is no opening that completely avoids tactics or completely avoids the necessity of strategic understanding.
For example, with the King's Indian, if you take the Classical Variation, Mar Del Plata, it's mostly a positional line where the center is locked and both sides advance on the sides in which their pawns point (the whole pawn pointing theory when the center is blocked, just like the French Defense), and then Black often has to sacrifice a piece at the end for the final breakthrough. Often times that's the Bishop on c8, hence why it's a cardinal sin to trade it off for another piece of White's. It needs to sacrifice itself on g4 or h3 in most cases.
Switch gears to the Fianchetto Variation, and it too is often a strategic, methodical game.
Switch gears to the Saemisch or Four Pawns Attack, and you often have to watch out for sharp tactics by White! Again, as I said, there is absolutely no avoiding it!
The same can be said for the Slav, QGD, QGA, you name it. For example, the Slav, often thought of as being solid, can get super crazy if White plays the 5.e4 line! 1.d4 d5 2.c4 c6 3.Nf3 Nf6 4.Nc3 dxc4 and now instead of the positional 5.a4, White plays the super sharp 5.e4. When I played the Slav, I've had crazier games from this than I have from openings like the Najdorf Sicilian!
Also, don't confuse the King's Indian with the Grunfeld. The Grunfeld has a higher ratio of "sharp" games than the King's Indian, but you can't avoid it completely!
Therefore, you'd be best off playing an opening with similarity to what you play against 1.e4 rather than simply avoiding tactics completely. The French and the King's Indian both follow extremely similar ideas. Block the center and then attack on the side in which your pawns point!
This is a common confusion with people. They get the completely wrong idea that just because BLACK'S PAWNS make the same moves in two openings that the two openings will be similar. That is a complete fallacy!
The chess board involves 64 squares and 32 pieces. Not 32 squares and 16 pieces that all happen to be Black. Take the King's Indian Defense and the Pirc Defense. Yes, BLACK plays ...d6 and ...g6 in both with an eventual ...c5 or ...e5. However, in one case, White has played c4, d4, and e4 (King's Indian) while in the other case, White has played d4 and e4, but the c-pawn has stayed home at c2 (Pirc). The difference in the White c-pawn alters the entire strategy of the game, and the two openings are NOTHING ALIKE from the overall perspective.
Think about Tic Tac Toe. Number the boxes 1 to 3 across the top, 4 to 6 across the middle, and 7 to 9 across the bottom. You are O, so you go second (just like Black in chess). To say that the King's Indian and Pirc, or French and Queen's Gambit Declined are similar is like saying that going in spot 3 on your first turn after White went in spot 5 on turn 1 would be the same as going in spot 3 on your first turn after White went in spot 1 on turn 1. They would not be similar at all. In the case of X going in spot 5 (the center box), going in spot 3 is fine (along with 1, 7, or 9) and you have a draw. In the case of X going in spot 1 (the upper-left corner), going anywhere except the center box is a loss for O. After X goes in 1, if O goes in 3, then X has 3 ways to win. He can go in 4, and after O blocks at 7, X blocks at 5 and has 2 ways out next turn, 6 or 9. A second option is he can go in 7, and after O blocks at 4, X goes in box 9 and has two ways out next turn in 5 or 8. The third option is X can go in 9, and after O blocks at 5, X blocks at 7 and has 2 ways out next turn in 4 or 8.
So don't get the misconception that just because Black happens to make the same first few moves that the openings are similar. They are not. Look at it from a strategic perspective. The French and the King's Indian have the same basic strategy. The center will be completely blocked, not just closed like the QGD, and so the strategy of what to do when the center is completely blocked, forcing play on the wings instead, is followed in both the French and the King's Indian. People will claim they are different because the French calls for Black to attack Queenside and the Classical King's Indian calls for Black to attack Kingside, but they are completely looking at it wrong. It's not about which side you attack. It's about following the same principles based on the blocked center. You are attacking the side in which the blocked pawns point! It's about the fact that the center is blocked and immobile. Take instead the Petroff, and you almost always have a completely open e-file, a lot like the Exchange French! Take the QGD and while the d-pawns block each other, it's all about pawn breaks and opening the center via neighboring pawns. When Black plays ...dxc4 and follows up with ...c5 or ...e5, the center opens. In the French, when Black plays ...c5, he may be chipping away at d4, but the center will still be blocked and there will still be a pawn on d4. It just won't be protected by a pawn on c3 any more and the c-file will be open. The center will still be blocked and it will still call for a queenside attack by Black since the blocked pawns (e6 and d5) point in that direction!
Hope this clarifies! Oh, and by the way, you talk about the light-squared bishop issue in the French and QGD. When comparing the French and the KID, you have the same problem in both openings. You have a very bad bishop. In the QGD, the ...e6-e5 advance opens up the Bishop. It's a lot harder in the French and KID. So what the bad bishop in the KID is the Dark-Squared one instead of the Light-Squared one. It's still a very bad Bishop all the same!
Understand the big picture, not the individual Black pieces, and you will see why the KID and French go hand in hand better than the French and QGD.
Don't let game count or results dictate. When you study the opening, do you actually UNDERSTAND what is going on? Memorizing 20 moves and understanding 20 moves are two totally different things!
I can spew out 12 moves of Exchange Grunfeld like the best of them, but I don't really understand it one iota. I've tried to play the Grunfeld. It makes no sense to me at all. Doesn't matter if I play 1 game, 50 games, or 100 games. I just don't get it.
For this exact reason, I don't play the Grunfeld. So what if I play 5 players that are 1500 and beat them all. It's not that I played the Grunfeld that made them lose. A 1500 player should lose to a 2100 the vast majority of the time. It has nothing to do with the opening.
On the flip side, I understand the nuts and bolts of what is going on in the King's Indian Defense, or the same can be said about me and the French Defense.
Don't let game count or one result sway you one way or another.