Here's my best opening as black after 1.e4:
A very tactical opening against 1.e4?

1.e4 e5 2.Nf3 Nc6 3.Bc4 Nd4? 4.Nxd4 exd4 5.c3 and White is already clearly better.
Other than that it's a great opening...
Agreed. I played a thematic tourney starting with 3. ... Nd4 and white has a large advantage that is easily felt. It is very hard to play with black and if white is a decent player and takes more than a few seconds considering the position he will not take the pawn.
I currently use the French Defense, but I find myself not doing too good with it at times and the cramped position is sometimes really annoying. Don't get me wrong, I like to use it and I've had some good games with it, but I'm just wondering if I should stick with it or use a different opening instead.
If I should change, which opening should I use?(And please don't tell me to use the Sicilian...)
If I should stick with it, what are good ways to deal with White's bishops constantly pinning my Knights and how should I deal with my Light-squared Bishop?
I use and have very good results with the French for the exact reason you want to get away form it. It works wonders against impatient tactical players.
I currently use the French Defense, but I find myself not doing too good with it at times and the cramped position is sometimes really annoying. Don't get me wrong, I like to use it and I've had some good games with it, but I'm just wondering if I should stick with it or use a different opening instead.
If I should change, which opening should I use?(And please don't tell me to use the Sicilian...)
If I should stick with it, what are good ways to deal with White's bishops constantly pinning my Knights and how should I deal with my Light-squared Bishop?
I use and have very good results with the French for the exact reason you want to get away form it. It works wonders against impatient tactical players.
lol, well it's not that I want to get away from it, it's that I'm wondering if I should stick with it :p
Anyway, the impatient players DO make the French Defense really fun to use. I guess I'll keep using it and see if I get better results.
A very tactical opening against 1.e4?
What about attacking the pawn right from the first move:
1. e4 d5 (Scandinavian Defense)
or
1. e4 Nf6 (Alekhine's Defence)

The French is a fine opening. Just see how the great players were handling the Black men: Botvinnik, Petrosian, Korchnoi, Uhlmann.
The "bad" white squared bishop is part of the overall positional trade of the opening, and can be handled in various ways.
Another idea is playing 1...e5. There the only worry is the Ruy Lopez, but even there Black can play sharply AND soundly- say what Shirov has named the "Tkachiev Variation": 1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Ba4 Nf6 5.0-0 b5 6.Bb3 Bc5.
I love playing that variation. I almost always play Bb7 later which transposes into the Archangelsk variation I think.

Here is another vote for the Alekhine defence. I use it all the time. But you have start trading pieces to get some room.
I currently use the French Defense, but I find myself not doing too good with it at times and the cramped position is sometimes really annoying. Don't get me wrong, I like to use it and I've had some good games with it, but I'm just wondering if I should stick with it or use a different opening instead.
If I should change, which opening should I use?(And please don't tell me to use the Sicilian...)
If I should stick with it, what are good ways to deal with White's bishops constantly pinning my Knights and how should I deal with my Light-squared Bishop?