Try manually selecting a network in your phone’s settings, rather than letting it select a network automatically.
You do have the correct APN, but it may simply be that the places you are travelling through in France have poor or no network coverage, which may be the case if you are travelling through rural area’s rather than large towns and cities.
If you are using a “mobile modem” AKA portable WiFi router, make you it’s not surrounded by metal, which would act as a faraday cage, blocking signals to the portable WiFi router. This can be an issue in caravans and motorbike homes, and is an issue that crops up fairly frequently during the spring and summer months on this forum.
