Suppose the Quasi War between the USA and France in the late 1790's had become a declared war? What would have happened? Especially, what would the UK have done? If the French fleet had tried to go to the USA would the Royal Navy have tried to stop it?
Would it have stayed rather a quasi war in reality given that the US hardly has the strength to take on the French at sea and not much real opportunity to face it on land.
On the other hand if the French got a fleet out into the Atlantic, the Royal Navy would not let it pass if it could help it. All going well it would be torn apart as just about every other French fleet that took to the seas during the revolutionary/naoleonic wars.
One thing that the French would do is send frigates out on cruises to to play merry hell with US commerce. But the Royal Navy and the US Navy would have done everything it could to play merry hell with these frigates.
It should make the US and the UK make common cause - imagine Edward Pellew and Stephen Decatur fighting side by side!