You are fine with French and QGD for Black.
I would remove the London and learn 2.c4. No reason to change all the way to 1.e4.
1.d4 and 2.c4, the main defenses you'd need a line against are:
QGA
QGD
Slav
Semi-Slav (unless you decide on Exchange Slav)
Nimzo-Indian
Grunfeld
King's Indian
Benoni/Benko
Dutch
Modern
Sure, there are others, but they are so rare that just making sure you have a playable line against each without having to go in depth should be sufficient. These include the Budapest, Chigorin, Englund Gambit, English Defense, etc.
I have a very narrow opening repertoire at the moment (London System as White, French Defense and QGD as Black). I'm afraid that this will stall my progress (especially playing the London System) and my goal is to become a much better player. I'm of course studying tactics, middlegames and endgames as well, so I'm not focusing only on studying openings.
I have heard that it's better to play classical openings to get better at chess in the long run. So should I switch to playing more classical openings for a couple of years to learn to play them well, before trying to learn other types of openings?
When I think about a classical repertoire, this types of openings comes to mind:
- White: 1.e4 with Ruy Lopez, Open Sicilians, Nc3 French, Advance Caro-Kann etc main line openings
- Black: 1.e4 e5 and going for the main lines
- Black: 1.d4 d5 and keeping the QGD as it is a very classical opening.
This kind of repertoire feels reasonable, but it definitely is a lot of work. But I'm willing to put in the effort, as I'm serious about my chess improvement. What are your thoughts? Is it worth the effort and will it really make my chess better?