The problem is usually not sending it OUT of the U.S., the problem may be in sending it INTO France.

A lot of European countries are extremely restrictive in terms of what gun parts can be send.  In Denmark, for example, the lower receiver is NOT the "critical" part of the firearm - it is often the barrel, or sometimes the barrel and bolt.  So, if you were asking about some guy in Denmark wanting to buy a barrel from overseas, it would almost certainly be a crime.

As another example - a number of years ago I wanted to send a couple of USGI mags to a guy in the Danish army who did me a favor.  After spending about four hours searching through various Danish customs sites and law sites, I discovered that it is in fact illegal for anyone other than gun manufacturers and licensed importers to receive any part of a magazine.  My point is, the only way I avoided sending some that was illegal under Danish law - and could be traced straight back to me - was to spend a lot of time trying to understand the laws in the receiving country.  I really would not like Danish authories calling their U.S. colleagues and telling them that I was vioalting laws and trying to "smuggle" something like "firearms components" illegally into the country.  


So unless you are either prepared to spend a lot of time looking into it (and learning to read French along the way), I've be very hesitant to send a gun aprt to another country - especially one in Europe.  HOWEVER, if the guy can point you to a specific legal document that says it is okay for you to ship a gun barrel INTO France, and you trust him, then go ahead.