Short answers, pulled from the story.
The Treaty of Versailles of 1768, concluded on the 15th of May 1768, was an agreement between the Republic of Genoa and France in which Genoa transferred Corsica to France. Genoa used the deal to settle debts it had no means of repaying, and France agreed to return the island of Capraia to Genoa as part of the terms.
Genoa sold Corsica because it was in financial decline and could not repay its debts any other way. The republic also lacked the military strength to suppress the Corsican independence movement, making continued rule over the island untenable.
Pasquale Paoli founded the Corsican Republic in 1755 and led the island's independence movement. His republic even occupied the neighboring island of Capraia, which France agreed to return to Genoa under the treaty's terms.
France began its conquest of Corsica in September 1768 and gained full military control following the Battle of Ponte Novu in 1769.
Genoa had ruled Corsica since 1284, meaning it held the island for roughly 484 years before ceding it under the 1768 Treaty of Versailles.
Until the French Revolution, Corsica was considered the personal possession of the French king rather than an ordinary province. France secured this status after its military victory at the Battle of Ponte Novu in 1769.