Is it right to say, "I wish to know how good your pick up on French is, since you are working in France." Can we use the phrase "pick up" as a noun?
Your proposed use of "pickup" as a noun is incorrect. There are two correct uses of "pickup" as a noun:
"Pickup" is short for "pickup truck". (This usage is common, and acceptable in all but the most formal contexts.)
A pickup truck typically has an enclosed cab and an open bed. The back of the cab is at the front of the bed. The bed has two short "sidewalls", and a "tailgate". It can typically carry one or two cubic yards of material. Depending on the make and model, the payload capacity can be anywhere from 750 to 2,500 pounds (300 - 1,100 kg).
Pickup trucks are often used by people who "pick up" loads, transport them somewhere, and drop them off.
"Pickup" is also an informal term for a discrete purchase or hiring. For example, a sports blogger might say, "That was a great pickup!" after his favorite team acquires a player on waivers. (In this scenario, another team "dropped" (fired) a player, and the blogger's team was able to hire the player.)