He'd fight one hell of a battle, but be betrayed by the same lousy suboordinates and low-quality Spanish ships that defeated Villenueve.
Each of the major French naval defeats from 1798-1805 were due to factors no admiral could stop. At the Nile, not only did Nelson's ships sneak between the French line and the shore where nobody thought possible, but the biggest French ship blew up, stopping any hope of reorganizing the French line. The Battle of the Saints wasn't really a defeat, as the French fleet was convoying a grain fleet which got through, and I can't see Jones doing anything that wasn't done OTL (fighting a fierce and close fleet-action lasting long enough to get the convoy out of harm's way). At Trafalgar, Villenueve had set up a reserve of 12 ships that were supposed to guard against breaks in the line by coming up to form a double line sandwiching any ships that got past, but the reserve was composed of spanish ships with fouled bottoms and incompetent crews, so they fell behind and couldn't prevent Nelson's strategy. Once again, there's nothing Jones could have done to overcome the lousy material he had to work with--his ship would fight to the last, but his fleet would fail.