Once France falls, a random number of French naval units will become Free French. The average is 15%. Once they become Free French, they are controlled by the UK regardless of what happens with Vichy France.
More often than not, I will send all the French units into the Med to attack the Italian Navy. If the British join in, it is sometimes possible to completely destroy the Italian navy. Against human players there are mixed results. Best I've ever done was to destroy the Italian sub and cruiser. Worst was to lose the French fleet with minimal damage to the Italian navy.
My view is that if the French navy hits the Italians hard, even if no Italian ship is sunk the Italians need to spend MPPs on reinforcing them.
Another option is use the French fleet to hunt German subs.
There isn't much to be gained by disbanding the French fleet, I feel. The damage they could do to the Italian fleet or the damage they could save the English fleet in sub chasing is worth more than the 120-140 MPP from disbanding them.
As for Malta ... I think that the UK needs all the air fleets it can get in the early stages. I keep the air fleet there until I think that the Axis are putting air fleets in place to hit it (causing some headache and hassle to the Axis) and the operate it out will transporting a Corp in. However, it has to be timed just right.