Réunion has a common history with Mauritius as part pf the Mascarene islands: 1st time reported on Arabic maps, maybe known by Swahili or Malay ancestors of Oceanic tribes, rediscovered by Portuguese explorers in beginning XVIth century (Mascarene is from Dom Pedro Mascarenhas)... and Réunion named as Santa Apolónia under Portuguese rule. But the island remained uninhabited.
1st French claims occurred from 1638 to 1642 when a dozen French mutinees injailed in Madagascar were deported in this island for several years. In 1649 the island was renamed in old French Isle de Bourbon in honour of the reigning dynasty of Louis XIV. The newly-founded French East India Company (Compagnie française pour le commerce des Indes orientales) decided in 1664-1665 to colonize Madagascar and Mascarene main islands. Only the Isles de France et de Bourbon (now Mauritius and Réunion) were successfully colonized. The island has been renamed a few times after the French Revolution: in 1793 the name Réunion appeared for the 1st time as a commemoration of the union between Marseille revolutionaries and Paris National Guard ; it was renamed again in 1801 Île Bonaparte in honour of the First Consul and future Emperor Napoléon Bonaparte, and again Isle de Bourbon after the Vienna Congress in 1815. Please note that the Royal Navy invaded both islands in 1810, and after this congress, the Île de France has been turned to English rule, becoming later Mauritius. The island was renamed a last time to its definitive name in 1848.
The 1st coinage, specific of both Isles de France et de Bourbon, appeared under Louis XVI in 1779 with a 3-year minting of billon coins of 3 sols/sous minted in Paris Mint (French mintmark A). No more circulating coins were minted for both islands before a 10-pound (Dix livres) silver coin made under the name of Îles de France et Bonaparte a few months before the British conquest. Please note, according to the CGB French website, this highly-rare coin was hand-made in the islands. The Paris mint sent a new 10 centimes billon coin to the newly-restored French colony of Isle de Bourbon, minted in 1816 only. No more specific coinage before the 1896 Réunion copper-nickel bond coins of 50 centimes and 1 franc, followed by aluminium notgeld in 1920. But most of the time, the island depended on national French coinage up to 1948 in which the French currencies were splitted between continental Europe (including Corse) and colonies. There is an ambiguity depending on websites, stating the island had the CFA or the CFP currency, but there is no ambiguity the island had its own coinage from 1948 to 1973, when the island became an Overseas region and turned back to the French national currency.
Please note, to finish this introduction, that as a French region, Réunion was part of the French regions program of €10 silver coins with 3 different coins minted from 2010 to 2012. These coins are legal tender in the whole French territory part of the eurozone, but official shipping was only available in the concerned regional post offices, like for other regions, including Guadeloupe, Martinique, French Guyana and Mayotte.
Napoleonic coinage from Îles de France et Bonaparte:
https://en.numista.com/catalogue/iles-de-france-et-bonaparte-1.html
Coinage from Isles de France et de Bourbon, Isle de Bourbon and Réunion:
https://en.numista.com/catalogue/reunion-1.html
Réunion coins from the French regions program:
https://en.numista.com/catalogue/index.php?r=&c=&co=y&cno=y&cc=y&cn=y&cj=y&ce=y&cu=y&cat=y&mode=avance&p=1&e=france&d=&km=&i=REUNION&v=10&m=&a=&t=&dg=&w=&g=&f=