The French Navy of 1940 was mostly obsolete, most ships were lightly armoured and not as well armed when compared to other navies.
The newer designs were the Richelieu Class which were modern but were also incomplete when the war began. The Dunkerque class were really just light weight battle cruisers.
And the the Aircraft Carrier Bearn was old and slow and was never really anything more than an aircraft transport. Even before the war France had no real naval aviation. Germany probably could have made no more use of her than the Free French Navy did…which was nothing but as an aircraft transport. She was also at sea at the time of the armistice with Germany and retreated to Martinique.
At best the French Navy could have added some strength to the Italian Navy but would have added ships no better and perhaps even worse than they already had. They certainly would not have been used any less unsuccessfully then the Italian Navy was already employed.
In German waters the French fleet would have been an added fuel drain on a already streched thin German fleet. German navy sorties were restricted by the lack of fuel far more than a lack of guts or the Royal Navy. And the Navy would have had to train more sailors to man these ships, placing a strain on the Reich’s manpower situation, which was also an issue. You simply can’t underman a ship so it seems unlikely the French Navy in German hands could have contributed much to any attempted Operation Sealion.
As successive German Navy bootcamps turned out sailors every 6 months or so, maybe the French fleet could have come on line and begun commerce raiding or added to a larger German presence in Norway or the Atlantic, but without real airpower the result could only be the same.
Big capital ships look pretty and look strong but with out fuel and a well trained crew they are just that.