How do you say registration in french?

It depends on the contest

As a noun

in school - a register is "Le cahier d'appel" or "le cahier de présence"

in a police station, or in a hôtel we say " un registre"

As a verb - If you consider the fact of adding something to a list, this is "inscrire"

- If you consider the fact of declaring something legally we say "déclarer" (To register one's birth = déclarer une naissance) - If you consider the fact of measuring something, we say "enregistrer" (the budget deficit registered a 10 billion dollars raising = Le budget enregistre un déficit de dix milliards de dollars) - If you consider the fact of showing a feeling or disapproval, we say "manifester" (His face registered disbelief - Son visage manifestait de l'incredulité) - if you consider the fact of declaring a vehicule, this is "immatriculer"

Hope this would help

Christophe