The French frigate scuttled after the 1760 Battle of Restigouche was Machault.
Le Machault sailed from Bordeaux in April 1760 carrying provisions and troops intended to reinforce New France after the British capture of Quebec. British naval forces intercepted the French flotilla in Chaleur Bay, forcing it upriver on the Restigouche.
After several days of fighting, French commander François de Giraudais recognized that he could not win a battle of attrition or safely preserve the cargo. On July 8, he ordered Le Machault and the merchant vessel Bienfaisant scuttled to prevent their capture. Marquis-de-Malauze was spared because prisoners were held aboard.
A common mix-up is treating every lost French vessel as a frigate. Machault was the frigate specifically named in the question; the battle also destroyed or captured merchant ships and smaller craft. The loss of the supply flotilla further weakened French resistance before Montreal surrendered in September 1760.