I do not know the specifics of France, but I fly frequently fly with both live and inert ammo. The basic rules for bringing live ammo on flights in the US and into the US are on the IAA website. I only fly with live ammunition into a foreign country like Holland or Germany or Switzerland or the Czech Republic when I have a permit. Different countries have different permit rules. The best place to start is the embassy for that country.
My experience with ammo that is obviously inert is that it is USUALLY not a problem. It must be in checked baggage. As far as I know, it is illegal everywhere to carry even inert ammo or ammo components onto an aircraft in the passanger cabin.
Some countries like Japan require a permit to possess even a single cartridge case so inert ammunition requires basically the same permit as live ammunition. I’m told there are other countries that have similar laws.
Before you bring ANY THING ammo related bringing ammo into France you should send a letter or email to the French embassy telling them exactly what you want to bring in and why. If they tell you that it is legal to bring in inert ammo or components, get that in writing and carry multiple copies when you travel, one copy with you and one copy packed with the inert items in your checked baggage. I am sure the screening will identify the items and people at one or both ends of the flight will search your bags that contain the inert items. Clearly mark the items as inert and leave them in a state where it is obvious, like bullets pulled and taped in reverse in the casemouth so they can be pulled and inspected. I perfer the primers be removed or snapped or have a hole drilled in them to show they are inert. Remember, few customs officers and most police do not have the experience with a range of ammunition that most collectors do.
Also check with your airline and tell them that you are carrying inert ammunition, and ask them to annotate it in the comments on your ticket record so that when someone sees the items on screening there are no surprises. Some airlines will not want to do this for you, but talk nice to them and explain that it sometimes prevents surprises or misunderstandings and they will usually do it.
DO NOT RELY ON THE ADVISE OF ANY INDIVIDUALS HERE ON THIS FORUM OR ANYWHERE ELSE, INCLUDING ME!!! CHECK WITH THE AIRLINES AND YOUR GOVERNMENT AND THE GOVERNMENT AT YOUR DESTINATION, AND GET THE ANSWERS IN WRITING.
Good luck on your travels.