@ThrillerFan - I agree wholeheartedly with the notion that "If you are only capable of playing one side, you don't know the opening", however, many openings for white have a classical theme while the proper defense is hypermodern, which is tricky for folks not familiar with both.
I play the Reti, and like you with the French Defense I am very comfortable playing both sides of it, but in that case, there's no classical element. I don't play the French Defense with black because of the bad light-square bishop that often results from the advance variation (3. e5). I had similar issues with the Nimzowitsch. Not that my results were awful with either one, but the patient maneuvering with limited space puts black on the defensive for far too long for my taste (though both defenses are fundamentally sound).
When I switched to the Owen Defense (which I know you dislike), though more accurately it's a baited French Defense which I transpose to the Owen (1. e4 e6 2. d4 b6), I had to take the time to approach it from both sides. The pawn-roller attempts (both e4-d4-c4 and e4-d4-f4) look formidable but can be effectively restrained, undermined, and then destroyed, and if 2. d4 is not played by white, black can immediately gain advantage in the center with 2. ..d5 (a favorable line of the French Defense) or 2. ..c5 (a favorable transposition to the Sicilian Defense).
For any given opening, you must know the principles of both attack & defense which are unique to that opening. Deviating from book moves is usually bad, but a player who doesn't know the opening principles won't usually be able to punish such mistakes, and will more likely make blunders of his own in reply.
what about for white?
Black? White? Who cares? If you know anything about an opening, you can play it from either side. If you are only capable of playing one side, you don't know the opening. You simply know how to parrot moves for one side. Player goes out of book, you are likely screwed!
French Defense all day baby! Give me White! Give me Black! Don't care! As White, I'll only play 3.Nc3 or 3.e5. The Tarrasch is a draw and the Exchange is garbage.
Want proof the exchange is garbage? I have a lifetime score of 62.5% here across 113 games (58% wins, 9% draws, 33% losses), and this only accounts for 1.e4 e6 2.d4 d5 3.exd5 - there are also games via 2.Nf3 d5 3.exd5 exd5 4.d4, and it's even better over the board. In the last 6 years, I've lost to the Exchange French once in a fast time control (G/30), and all other games (roughly 20 to 30 total), are wins and draws.