Could you clarify your question? If I'm reading between the lines properly I think you're asking why they didn't take any territory during the combined invasion of France in 1940.

Is that correct?

If that's the case, then the answer is that they did. There was a very small region of France that was occupied by Italian forces around the area of Nice after France's surrender in 1940. When Germany moved to occupy Vichy France in 1942 with Case Anton the Italians expanded their territory, moving the border of Italy in Southern France to the edges of (but not encompassing) Marseille and Lyon while also occupying the island of Corsica.

Of course, that situation pertained for only 8 months until Italy left the Axis via signing an armistice following the Allied invasion of Italy.