Italy could definetily use the economic boost, but it makes much more sense to give it to Germany. Germany is only given 30 ipc’s to start the game out, putting it virtually on par with the London Brits and far behind the Ruskies. Germany is also the most critical and important axis player (japan is a close second) as they start out right in the middle of the fight and face the full brunt of the British and Russians and often times the Americans like to go for Germany too.
Therefore the Germans need France, it is a crucial part of the axis strategy, if the Italians were to take it they would probably either spend it all on a fleet, which would not be able to raise a finger against the american/anglo fleet, or spend it on ground units to take the fight to russia but would still be playing the minor role on the eastern front.
Germany also makes more sense strategically in taking france because they can afford to spend 3 infantry a turn in Paris to build up the atlantic wall while fighting the russians in the east, where as usually the Italian player is spending all of their money trying to take Cairo/africa, which under the direction of an experienced british player, can be very hard to take.