French is often not as compact as English (really, 5 more chars is too much ?)
- Connexion is slightly shorter
- Maybe ‘Entrer’ (Enter) would reasonably mean the same to you ?
- Or if the ID box is right after, simply ‘Nom:’ (Name:)
I’m afraid you’ll have to design larger buttons… but the more I think about it, ‘signer’, though uncommon, would be readily understood especially when opposed to ‘s’inscrire’. At least for me if I chanced upon it.