One of the less discussed features of the late 18th and early 19th centuries is the hostility towards Britain on the part of the rest of Europe. The American Revolution saw the British at war with the French, the Spanish, the Dutch, fand aced with a hostile league of neutrality led by Catherine the Great. During the Napoleonic War, Russia went to war or almost did with: Russia, Prussia, the Ottoman Empire, France, Spain, the United States of America, and Denmark. (Presumably its failure to go to war with Austria can be tied to its relative lack of a coastline).
Europeans and Americans were under no illusions; there was a real feeling that Britain was pursuing continental hegemony of its own, through control of the continent's overseas commerce. (This was one of the reasons that the Austrians weren't opposed to France keeping Flanders; it was assumed a French Scheldt would pressure Britain).
How feasible is a more savvy French republic exploiting this, and making the war appear to be a struggle against the despots of Britannia? Maybe getting the US toj oin the League of Armed Neutrality?