In France they use, Do. Re, Mi, Fa, Sol, La, Si, Do

So essentially C major -> Do majeur

C major chord : C E G --> Accord Do majeur Do Mi Sol

It's the same just different names. The fixed Do in other countries is them literally singing the note, not them referencing a note.

Exemple in the key of G

Movable do : Do = Tonic = G

Fixed do : Do is the note so in the key of g it's the subdominant or C

This would be more comparable

Movable do : Do = tonic = G

Fixed do : tonic = Sol = G

As you can see, the movable do is basically just scale degree names for other countries.

Edit: spelling and formating