I have been using an Android phone for quite some time now and always had an issue with the French characters when texting (if was often showing as question mark). The very strange thing is that I was able to read them without any issues.

I found a solution today.

instead of using the default SMS application, I have downloaded the free Textra from Delicious (https://play.google.com/store/apps/details?id=com.textra).

Now everybody can read my messages correctly.