More ways that Napoleon not coming to power might help here -- the Italian Republic is now unlikely to have the same head of government as France (even if
their President is still Napoleon); and the Batvarian Republic is now less likely to have a reactionary coup in 1801; and negotions following the tentative peace deal in September 1801 won't have the Bonaparts trying to put the screws on Cornwalis (though Talleyrand will still be there, so possibly not so different). AAR, less tension on issues of the Lowlands and Italy would mean that the intervention in Switzerland isn't as much of a provocation (which, taken in itself, isn't such a big deal, since it ended with a negotiated settlement).
CONSOLIDATION:
Depends how France is run. Effectively France was seen (due to the Terror and subsequent actions) as a "Rogue State" as it were, and in the early 1800s there was a hope that it had stabilized (though this came to naught OTL).
What, specifically, are the British looking for in how France is run to consider them sufficiently stabilized?