Réunion Island is an Overseas Department of France.
Depending on your citizenship, a specific visa may be required to visit Réunion Island.
Several countries are also exempted from visa for Réunion Island.
When applying for the Schengen visa, an EXTENSION to Réunion Island should be specified ("Valid for Reunion Island").
Visa information (in French language) for Réunion Island is available at:
https://www.legifrance.gouv.fr