Here are some statistics of white's score from my DB:
Both players 1.e4          1.e4 e6
2700+          55.8%       60.6%
2600+          57.1%       60.7%
2500-2600    54.6%       54.8%
2400-2500    54.7%       55.3%
2300-2400    54.3%       54.7%

...
more important data 

....

The first statistic that popped up is bad news for the French: With both opponents above 2700, the French scored 61%-39% for White (with a 44% drawing ratio, 11% less than the figure for all games), whereas 2700+ games in all openings had a 56%-44% ratio. Although this basically means that in a 20 games tournament Black would be only a point behind using the French instead of a generic opening, that is still quite significant, and the performance rating advantage for White is greater than White's normal advantage in the 2700+ database by 60 points, which is certainly nontrivial. The sample space was rather small, however, and this led me to wonder about the breakdown of these games. I have noticed for years that the elite players, who are frequently involved in closed events, have had a tendency to use the 3...dxe4 versions of the French to try to draw as Black (and taking short draws). In fact, no less than 30% of these 2700+ games are in those variations, as opposed to merely 8% of 3...dxe4 Frenches in Megabase as a whole. And the results for those variations were poor, as with other passive lines; whereas a more dynamic line, the Winawer Variation, had a 54%-46% ratio and 42-point rating spread, both of which are actually better for Black than for all the games in this 2700+ database. I've noticed before that when these top players use an opening to draw as Black (like the 3...dxe4 systems), they indeed get more draws, but have a mediocre or worse performance. The Petroff Defence, for example, draws at a spectacular rate, but performs a bit worse for Black than the average defense at 2700+ levels (and worse than that at lower levels). You'd think a high percentage of draws would help Black's performance rating; but I think that 2700+ players using the Petroff tend to accept the draw when offered, even if they have a small advantage, whereas with White they are more inclined to play for a win. Similarly, players at 2700+ may need to employ the French with more ambition in order to improve its performance - in my opinion, it isn't a very good drawing weapon.

The news gets much better for Black in the 2600-2699 region, with of course a much larger sample space. Now using the French results in a 57%-43% spread, one point worse than in the 2600 database as a whole (equivalent to 1 more loss in 100 games), and because of the rating differential the performance rating spread is only 9 points lower than the average of other openings (having the Sicilian Defence in the pool accounts for more than this gap.) In fact, this performance is as good as or better than other 1 e4 defences. Curiously, using the example above, the Petroff does poorly at this level with 59%-41% and a 41 point performance rating deficit below normal, even with a very large sample of games. I suspect that the same people questioning the 'correctness' of the French wouldn't assess the Petroff in the same way.

Finally, for all games in Megabase, the French produces nearly identical results as the database as a whole, and does better than most individual 1 e4 openings (because the Sicilian at 51%-49%, and taking up over 20% of all chess games played, makes the others look bad!). That includes, for example, the traditional Ruy Lopez after 3...a6 4 Ba4, considered about as sound as it gets. I should also say that, as was pointed out in the Forum, the French does as well or better than major 1 d4 defences (usually about the same).

My conclusions: The French has indeed performed worse than the average opening at the 2700+ level; I think that's at least partially explicable by a skewed choice of variations (within a very small sample space), and not too worrisome. On the positive side, it does well in all other ranges (up to 2700). At any rate, I think it's fair to call the French 'correct'; if it isn't, then arguably nothing besides the Sicilian Defence is! Still, I haven't put a great deal of time into this investigation, so you may want to generate your own figures, use other criteria, or challenge the assumptions. Forum material, perhaps?

I tend to agree with Markovich. If 1...e6 can just be declared somewhat bad for Black by a bunch of patzers like us, what hope does chess have period? Play what you like an don't worry about the popularity at the top level. Bent Larsen played all kinds of unpopular things and was one of the most successful tournament players ever. I can think of 3-4 masters in my area of Ohio alone that only play the French and are extraordinarily successful. 

I think the only problem with the French is that it is out of fashion as a means of achieving a winning, unbalanced position. Right now the Sicilian seems to offer more opportunities for a Black victory in the eyes of the chess world. If semi-closed openings were so bad for Black then why is the Caro-Kann so popular at present? ...[snipped]

I remember Grandmaster Bareev coming to Southern California and, during a lecture, telling us that the French Defense was "not correct." And that was coming from a fan. 

After playing the French for a long time and examining hundreds of master games, I tend to agree with him. There are bright spots, such as Shulman and Grischuk's handling of the Poison Pawn Winawer. Most variations after 3.Nd2 and especially Nc3 favor White. When a defense loses it's popularity it's because it becomes difficult to win with and because it lacks a champion to show the way. It just seems to me that many lines are a pain to defend and White now possesses the theory (given all the computers out there) and technical know-how to execute Black in would would ordinarily be inferior but messy positions. 
This doesn't mean it can't be played against 2000 ELO players though.