Dueling pistols broadly lacked rifling but this English one had a unique hidden form of rifling called 'French Rifling'. The idea was during a duel the pistols would be inspected for rifling to ensure neither side was cheating. But French rifling wouldn't be seen, allowing one party an unfair advantage.
French rifling wouldn't go the full length of the barrel so all but a thorough examination would suggest the gun was smooth bore.
Jonathan Ferguson from the English Royal Armouries Museum suggested that the name came from the English associating French people as being underhanded, rather than French usage of the rifling.
Own a musket for home defense, since that's what the founding fathers intended. Four ruffians break into my house. "What the devil?" As I grab my powdered wig and Kentucky rifle. Blow a golf ball sized hole through the first man, he's dead on the spot. Draw my pistol on the second man, miss him entirely because it's smoothbore and nails the neighbors dog. I have to resort to the cannon mounted at the top of the stairs loaded with grape shot, "Tally ho lads" the grape shot shreds two men in the blast, the sound and extra shrapnel set off car alarms. Fix bayonet and charge the last terrified rapscallion. He Bleeds out waiting on the police to arrive since triangular bayonet wounds are impossible to stitch up. Just as the founding fathers intended.
So the English created a cheat, and then named it after the French because they perceived the French as cheaters. The lack of self awareness is staggering.
Johnathan mentioned in the video the rules of dueling would be agreed upon by the duelists. So a cheater might arrange for an opportunity to swap them or perhaps have a third party (that he bribed) pick them.
I wonder if one would normally aim a non-rifled pistol differently, so that if your opponent got the rifled pistol they would be likely to miss their shot.