It depends. Britain was supportive of a move to French constitutional monarchy, which quickly turned hostile when the revolution went full Republican.
But it still depends on Frances position itself, as long as the overall status quo is held Britain will be happy to sit back and trade while waiting for the next round of colonial wars against the 'old rivals' of France and Spain while maintaining short-term allies on the continent.
If France feels the need to flex its proverbial muscles, or other countries begin mocking the French Monarchy and prestige over the Monarchy's reduced position then war will likely follow, though maybe not to the radical degree of the Wars of Coalition. (If I remember right Britain wasn't seen as a 'real' monarchy at the time and hadn't since the Civil War due to Parliaments dominance. France may face similar thoughts and opinions.)