I believe you have a parts gun. And while its not impossible the French might have used it, and put the star on it, its a cobbled together gun.
I have found reports that the French did run some German factories until about the end of 46, and built perhaps as many as 50 Panther tanks and a couple hundred FW 190 fighter planes. They did make many thousands of Walthers, especially P.38s.
I can find no reports of them producing Lugers. This doesn't mean that a handful of guns couldn't have been assembled with whatever parts they could find, but I can't find any mention of it being an organized thing like the production of P.38s
The frame of the gun pictured says "Germany" on it. This marking was only applied to pre WWII guns intended for commercial sale. The chamber appears to have the date of 1939. The barrel and the forward part of the toggle assembly have the Nazi Eagle stamp, meaning that those parts (at the least) went through the Nazi system either before or during WWII.
Also, the 3 digit serial number is suspect. The standard practice was 4 digit number that repeated in blocks with a letter added after the first block.
And the normal place for the serial number was on the front frame below the barrel, not on the side of the chamber.
ok, I checked the link, and I stand corrected. Apparently there were a number of Lugers put together under French direction. Wonder why none of my references mention that....
Germany stopped producing Lugers in 1942. The tooling was "repurposed" we would say today. Germany stopped making Lugers so they could use the tools and workers for other, more cost effective projects.
When Mauser wanted to produce Lugers again, for civilian sale, they wound up buying the tooling from the Swiss, (who had stopped making Lugers a long time before, but still had the tooling in storage,) as it was the only existing tooling. This is why Mauser made the "Swiss Pattern" Lugers for a limited run in the 70s. The original German tooling was long gone.