Revolutionary France was starving in the spring of 1794. The harvest had failed. To feed Paris, the Republic turned to its American colonies and to the young United States, which began assembling an enormous grain convoy in Hampton Roads. To shepherd it home, the French Navy sent most of its Atlantic Fleet to sea that May, scattered across the ocean in squadrons under the overall direction of Louis Thomas Villaret de Joyeuse. Among the independent cruisers were the Atalante and the corvette Levrette, prowling for British merchant ships. On 5 May, three days out from Cork, they spotted sails on the horizon. They closed to investigate. It was the worst kind of luck. The convoy they had stumbled on was escorted by two ships of the line.

At 17:45 on the 5th, Captain Charles Boyles of Swiftsure turned toward the strangers with HMS St Albans, a 64-gun ship, alongside him. Swiftsure hoisted her colours and fired three shots in the direction of the larger Frenchman. Linois understood his error at once. He raised the tricolour, ordered all sail, and ran. The two French ships split, and the two British ships split with them, each chasing one. Levrette outsailed St Albans through the night and escaped after dark. Linois could not shake Swiftsure. By 02:00 it was clear his manoeuvres had only slowed him down. Boyles closed steadily through the dark hours, came within range at 02:30, and opened fire. The fight was over in under an hour.

Linois lost ten of his 274 men and had 32 wounded. Swiftsure lost one. Boyles put a prize crew aboard the captured frigate and took the surviving French sailors aboard his own ship as prisoners of war. The Royal Navy already had a vessel named HMS Atalanta in service, so the captured Atalante was renamed HMS Espion and would later serve under the British flag as a 36-gun frigate. Linois himself was treated as a man who had done his duty exceptionally well. The naval historian William James wrote in 1827 that Linois's 'endeavours were highly meritorious,' and that against a British frigate of equal force 'the Atalante, if conquered at all, would have been dearly purchased.' Linois was exchanged shortly after reaching Britain and returned to France to fight again.

The action of 7 May 1794 was a minor engagement. It was eclipsed within a month by the Glorious First of June, the great fleet battle that climaxed the Atlantic campaign of May 1794. Yet Linois's reputation, polished by his refusal to surrender easily, helped carry him to a notable career in the wars that followed. The pursuit of his small ship through one long night and into the dark before dawn became one of those incidents that naval historians remembered because of how it was fought rather than what it decided. On the day itself, a French battle squadron from the larger Atlantic operation chased both British ships through the rest of the daylight hours. Both eventually escaped under cover of darkness, the grain convoy slipped away, and the Atlantic kept its silence over the ten French sailors who had not lived to see the morning.