I think having a coach go over your strengths and weaknesses would be the best way to elicit good feedback. Barring that, I've taken a look at a smattering of your rapid games and have some suggestions for you:
White:
Have you considered opening with 1.d4 or 1.c4? I notice that you don't have many tendencies to attack your opponent's king -- likewise you seem to come under a lot of pressure when your opponent fully commits to attacking you. There's usually deferred action against kings especially with 1.c4, which may be more comfortable for you when positional play is at more of a premium.
Black against 1.e4:
I notice that sometimes your king comes under a lot of pressure in this opening. In one game I looked at you played the Taimanov Sicilian (1.e4 c5 2.Nf3 e6 3.d4 cd4 4.Nc6) and seemed to understand how to play the opening well. I've played the Taimanov and related ...e6 Sicilians for quite awhile and can say that I've been happy with that choice. Although attacking positions can always arise in the Sicilian, I would venture to say that you might find the defensive resources of the Taimanov more natural than those in the French.
Black against 1.d4:
It seems like of all the areas in which you're needing a new repertoire this is probably it.
You had a couple interesting games in the French where you creatively shuffled your pieces around behind your pawns (including a king walk over to the queenside) that reminded me of the kind of maneuvering I'd normally see in a Nimzo-Indian. As with the Sicilian, you must still defend kingside attacks from time to time in the Nimzo, but again you have quite a few defensive resources. Black's plans in the Nimzo, while various, might be more clear to you than the classical (1.d4 d5) structures you've been playing. Your play on the black side of double queen-pawn openings doesn't feel very inspired so it might be good to switch to 1...Nf6.
You can also play Nimzo ideas against the English, which would otherwise target your 1...d5 repertoire.
Sidelines and irregular openings:
They come up and at some point you'll have to learn them. The best advice I can give you here is that certain sidelines come up more often than others and generally require more strict memorization than main lines. Don't waste time learning all the obscure lines that your opponents can play -- instead focus on the most popular lines and learn them well. Some examples:
Smith-Morra gambit - very popular, many tactical traps but black's main line choice, while requiring memorization, will give you a clear path every time you face the opening.
Other anti-Sicilans - the nice thing about the Taimanov Sicilian and other ...e6 Sicilians is that they are generally quite robust against Anti-Sicilians. It would be good to have lines ready against the Grand Prix and Closed Sicilian.
Kingside fianchetto (white) - including the KIA and English, it's probably best to have a single system (if you play the Nimzo, including ...Nf6 and ...e6) that you can rely on against these openings. They're not typically very interactive (white plays the first few moves in his own little world) so any setup you choose should not require a lot of study.
London/Stonewall - openings that employ the c3-d4-e3 pawn structure require some study in their own right because they deviate from white's regular 1.d4 spacegrabbing. Typically a single main line can be memorized from the black perspective to get an adequate position.
I think having a coach go over your strengths and weaknesses would be the best way to elicit good feedback. Barring that, I've taken a look at a smattering of your rapid games and have some suggestions for you:
White:
Have you considered opening with 1.d4 or 1.c4? I notice that you don't have many tendencies to attack your opponent's king -- likewise you seem to come under a lot of pressure when your opponent fully commits to attacking you. There's usually deferred action against kings especially with 1.c4, which may be more comfortable for you when positional play is at more of a premium.
Black against 1.e4:
I notice that sometimes your king comes under a lot of pressure in this opening. In one game I looked at you played the Taimanov Sicilian (1.e4 c5 2.Nf3 e6 3.d4 cd4 4.Nc6) and seemed to understand how to play the opening well. I've played the Taimanov and related ...e6 Sicilians for quite awhile and can say that I've been happy with that choice. Although attacking positions can always arise in the Sicilian, I would venture to say that you might find the defensive resources of the Taimanov more natural than those in the French.
Black against 1.d4:
It seems like of all the areas in which you're needing a new repertoire this is probably it.
You had a couple interesting games in the French where you creatively shuffled your pieces around behind your pawns (including a king walk over to the queenside) that reminded me of the kind of maneuvering I'd normally see in a Nimzo-Indian. As with the Sicilian, you must still defend kingside attacks from time to time in the Nimzo, but again you have quite a few defensive resources. Black's plans in the Nimzo, while various, might be more clear to you than the classical (1.d4 d5) structures you've been playing. Your play on the black side of double queen-pawn openings doesn't feel very inspired so it might be good to switch to 1...Nf6.
You can also play Nimzo ideas against the English, which would otherwise target your 1...d5 repertoire.
Sidelines and irregular openings:
They come up and at some point you'll have to learn them. The best advice I can give you here is that certain sidelines come up more often than others and generally require more strict memorization than main lines. Don't waste time learning all the obscure lines that your opponents can play -- instead focus on the most popular lines and learn them well. Some examples:
Smith-Morra gambit - very popular, many tactical traps but black's main line choice, while requiring memorization, will give you a clear path every time you face the opening.
Other anti-Sicilans - the nice thing about the Taimanov Sicilian and other ...e6 Sicilians is that they are generally quite robust against Anti-Sicilians. It would be good to have lines ready against the Grand Prix and Closed Sicilian.
Kingside fianchetto (white) - including the KIA and English, it's probably best to have a single system (if you play the Nimzo, including ...Nf6 and ...e6) that you can rely on against these openings. They're not typically very interactive (white plays the first few moves in his own little world) so any setup you choose should not require a lot of study.
London/Stonewall - openings that employ the c3-d4-e3 pawn structure require some study in their own right because they deviate from white's regular 1.d4 spacegrabbing. Typically a single main line can be memorized from the black perspective to get an adequate position.