The biggest problem for small compromises is that the compromises aren't that small. The Parliement need new taxes to be levied, but they don't want to give the Americans representation.
Parliament didn't have one monolithic view. Plenty of people in it sided with the colonists and thought they should have representation, including various big players. A little more moderation from the colonists, and eventually the more progressives Whigs would have formed an administration and given them it.
The Colonists wanted representation if they were to pay new taxes (which could be also a fact that they just don't wanted to pay any taxes, knowing the American state of mind

). What compromise do you propose ?
Various things could have been done. Ask for block grants from colonial treasuries to pay for the common defence, rather than direct taxes. Appointing a few prominent colonists to the House of Lords. Giving representatives of the colonial assemblies annual meetings with the Privy Council.
Knowing that George III think that beig lenient with the colonist would be a sign of weakness.
That's a ridiculous statement. Allowing some reform would have been greatly welcomed. This is an anachronistic attitude that the Americans hated the British and were just trying to get away from them. A lot of people on both sides want reconciliation, but there was just a bit too much stubborness on both sides (particularly on the British). Changed incentives would do a lot.
And for the "fear" of the french, a few victories were won by the Militias against the French in the 7 years war, they know that the French colonies aren't so much populated, and they smuggled with the French.
Sure, it wasn't as big as the British colonies, but Canada was pretty large, and more importantly, it was part of a global empire with a powerful navy. Not to mention an empire that has increased co-operation with the Spanish who also have a very powerful navy.
Tyr and Socrates both seem to me to have basically agreed:
Er, but both France and Spain were STILL at our door at the start of the Revolution, and yet we somehow chose that terrible risk (not!) of existing.
You might want to check your geography. There were no French or Spanish population centers anywhere near US population centers at the time of independence. Whereas in Canada they were just over the hills from New England.
I recommend reading our Declaration of Independence - we weren't without reason.
Colonies have grievances shock. This has happened plenty of times without it coming to all out blows: look at Canada in 1837. But what happened? The British were more tolerant because they worried about the foreign power just next door - the same situation we'd still have if the French were there.
Summary: Georgie 3 was a lamer and turned long benevolent neglect into war by dumb aggression.
There I was treating history as something other than partisan frat-boy contest. My mistake.
On the questions of French colonial fate, I think that in the Nappy case, he's likeliest sell New France along with Louisiana because of the facts pointed out upthread about Royalist officials already dominating and his OTL wish to shift troops from NA to Europe as well as his want for $$. Other cases take some thinking.
Napoleon sold Louisiana because he didn't have a hope of holding onto it otherwise. That's simply not the case with Canada. If anything he'll be looking to expand into the Ohio valley and make the US a puppet state of the French Empire.
90.000 inhabitants an immediate threat ? To 1.5 millions americans ? Ok give it 200.000 assuming a huge emigration movement after the 7 years war. No, still not a threat to me.
You mean in the same way it wasn't a threat when the British used it as a base to invade the US and set alight to Washington?
And again, even with the "threat" of France, who is going to compromise first ? The American ? Their is no middle way between representation and non-representation. And the English?
It doesn't so much need both sides to back down as for neither side to be so strident in the first place. There are plenty of middle ways between representation and non-representation, as mentioned above: appoint a few malleable Lords; a formal voice in Washington that meets with the privy council, even if outside parliament, etc. There are also compromises on taxation: a lower level of new taxes, a request for a payment to be collected however the colonial assembly saw fit, contribution of troops to a regular army in lieu. Plus other things could be thrown into the bag, like less enforcement of the prohibition of trading with foreign empires etc. Will it be enough to entirely satisfy the colonists? No. Will it be enough to satisfy the colonists that if they keep pushing they will win more reforms, and thus not resort to an independence war? Yes.
Everyone would see them as weak, as they don't have the strength to assert their will on some colonist. Giving them representation would damage the prestige of Britain among the european powers.
Since when has Britain cared what foreign powers thought? The continental absolutists had always thought of British constitutionalism, and giving rights to parliament as week. The British didn't care for a moment, as they saw it as a spirit of liberty. They would paint expanding rights for Englishmen in America as the same thing.
And it would cause a great uproar on the home islands.
Firstly, it wouldn't, as most Brits were pretty ambivalent about the issue, but were generally more supportive than not before the Boston Tea Party inflamed attitudes. Secondly, British public opinion was completely hostile to giving rights to Catholics, yet it didn't stop those reforms.
I suspect this would go the opposite way. Imagine a Britain that gives up New France after the war for Cuba or Martinique. British posters ignore, for some reason, that Americans did contribute to the 7 Years War and were taxed for it. Imagine the feelings here.
Yeah, the colonists would be annoyed by this. But they had previously had to give land back to New France in previous wars. What happened is that they got annoyed and then calmed down as it wasn't a lasting grievance. Also, the British are going to at least keep the Ohio country, which was the main aim of the colonists, so they won't have too many frustrations. Particularly as they wouldn't be able to take Canada without British help.