First raised as a regular French unit in 1635, La Marine had 4 battalions. Cardinal Mazarin raised the original unit and was able to have it made one of the Vieux Corps, so from ranking 16th the regiment became the 6th. It was at Hastenbeck in July 1757 and then Rossbach in November, where it covered the retreat of the Allied army, having not been engaged in the battle itself. It had a busy time in minor and not so minor operations until the battle of Krefeld, June 23rd 1758, where it was distinguished defending the woods along the Niers River before retiring in the face of much superior forces. At Lutterberg in October 1758 the regiment was barely engaged in the fighting. In April 1759 it returned to France to help protect Le Havre against a threatened British attack. For most of the rest of the war it was stationed in various French garrisons, apart from a detachment that embarked on an expedition to capture St John's in Newfoundland in May 1762. Although the French force captured the place it was forced to surrender to a British relief force in September and all the French troops became POWs.
The flags as depicted were carried by this regiment from 1636 to 1791.
And this plate shows the uniform and flags in 1757: