Réunion Island is an Overseas Department of France.
Depending on your citizenship a specific visa may be required to visit Réunion Island.
Visa information (in French language) for Réunion Island is available at:
You may also find some useful information about visa requirements for different countries at:
http://www.consulfrance-newyork.org/Do-I-need-a-visa-Click-to-select-your-country