French troops invaded Corsica in 1738, then left in 1741, only to come back in 1756, under the cover of acting for Genova. They kept garnisons in coastal towns until the formal annexation and the subsequent war. Napoléon's parents were married under Paoli's orders, as he wanted to unite pro-independence families. He was conceived during the war (his mother was famously pregnant with him in the last times of the Corsican resistance), so his birth is directly determined by the french intervention.
As I wrote earlier, evacuation of Corsica by the Austro-British-Savoy was a direct consequence of the peace talks, in which Louis XV agreed to withdraw from the Austrian NL in exchange for the ending of occupation of France ´s italian allies. As we know, Paoli was quite willing to ally himself with the British in order to keep Corsica free. He would probably play the same card in the 1750'.