Anyone who saw that semi-final... When Nadal decides to bully your FH when you're both right-handed AND have a one-hander, there's a problem. Either your 1HBH is so godly that Nadal doesn't want to waste time even bothering attacking it, either your FH sucks. Or both. That match showed us what happens when he is denied the use of his BH by a very high level opponent. His FH isn't good enough to be a viable alternative, or at least be able to redirect the rally towards Nadal's BH which is really solid but not a monster either.
Moreover, you don't happen to win two 5 setters back to back with a lack of mental. Especially against Ferrer against whom he had a terrible mental complex and H2H [2-8]. I'm too lazy to find and translates some French interviews of it, but it's well known that Gasquet has/had mental problems against Ferrer.
I also think that his problem ain't fitness. His very good early preparation in the off-season 12/13 showed good results, and his much better fitness allowed him to regain his top 10 rank. Previously, he used to build physical shape during the season. This time he was ready from the get-go, which is much better than before. Of course it ain't perfect, but it is an area where he significantly improved this year. Of course there was that ankle injury that costs him some ATP race point earlier this year, but that's what you earn by playing very often on slow hardcourts.
At this point of time, it's more than time he modifies his FH, it's costing him matches. It's more than a decent enough shot against lower level opponents, but it's clearly not enough against higher level players. To be fair, I dislike the question of the OP, or any kind of question that resembles it. But I also think Ferrer's FH is more solid than Gasquet's in tight moments and that it would be an improvement to have a similar one. Gasquet happens to have a FH that sits between the "modern" one and the "classic" one: lack of "pat the dog", old-school wind-up but using a WW finish. DelPotro can make it work, but he ain't named the "Tower of Tandil" for nothing.
I'd indeed modify his FH to be a totally modern stroke, using his core muscles much more, having a proper "pat the dog" in his backswing and all the yadda-yadda you may already know if you're crazy enough to visit the Tips and Instruction forum.