There was a much closer example to the French republicans of revolution and the absence of Kings - the Netherlands. Stadthoulder was never quite the same as King and the Patriots had been engaged in military conflict with the Stadthoulder as late as 1787. They lost but they hadn't gone away (and were residing in France mostly).
The notion of absolute Kingship wasn't as ingrained in French psyche as it was in Louis XIV's time.
Except the genuinely republican stadtholdlerateless period was seen to have been a failure that saw the Dutch collapse as a great power. You are right that absolute monarchy wasn't engrained (not least because the British had done so well with a limited monarch, even more so ITTL), but a true republic was seen as something that doesn't really work outside city states.
If France gets so far as revolution (which I am sceptical about, but is possible), they are much more likely to try constitutional monarchy with Louis XVI, and if that doesn't work, try another King, like the Brits did.