Though Réunion is a French department, it’s not part of the Schengen treaty. The visa requirements for entry to Réunion are almost the same as for France, bar a few exceptions. For EU nationals, a national ID or a passport suffices. Citizens of a number of other Western countries, including Australia, the USA, Canada and New Zealand do not need visas to visit Réunion as tourists for up to three months; they need only a passport.
Other nationals should check with the French embassy or consulate nearest your home address to find out if you need a visa. For example, Brazilian citizens do not need a visa to enter mainland France but do require a visa for Réunion.
Except for EU nationals, those who don’t need a visa and wish to stay for longer than three months need to apply for a carte de séjour (residence permit). Contact the Service des Étrangers (0262 40 77 77; 4 Place de la Préfecture) at the Préfecture in St-Denis.