Probably the wrong Champvalliers - there are several. It is the Champvallier north of 03190 Nassigny. Unfortunately, I don't have the co-ordinates. Long time ago I have been there. Very remote - not even on street view or similar.
Please, have a look on https://www.kunstgeografie.nl/centres/centre.mich.htm
Champvallier north of 03190 Nassigny is the most recent accepted estimation of the geographical center of France (corresponds to your picture).
The monument at the crossing of the village of Bruère-Allichamps is a historical estimation of the geographical center of France but the most visited one (corresponds to the picture from JON12A).
Have a look at this. I agree with Ralf that the sign is near Nassigny I still think it is on the road to Champvallier which is a tiny hamlet to the north west.
continuing the search for coordinates....it looks like the road between Nassigny and Champviller is the route de centre de France as it's calles is the place to search for it.....tough one to find sofar but not giving up on it.....good training computer skills.....which are none....at best....
https://www.google.pt/maps/place/46...0x0:0x0!7e2!8m2!3d46.5118074!4d2.576527?hl=nl
Some info tells me it shud be a little north of Champvilliers and this is a spot which could be it but unsure and cant get streetview to check.....so I'll go there in febr to make sure the coordinates are OK ...this spot is N46 30.42.5 and E 2 34 35.5 some strange method of coord that google gives me....why is there not 1 system to do coordinates but several which I cannot translate into some normal that BC can read!!!
I used your link, then copied the coordinates that Google maps gives me in the Link address, see below, I then copy and paste into Basecamp, works a charm every time.