During the Anglo-French War of 1627-1629, itself a part of the Thirty Years' War, the English sent an adventurer David Kirke and his troops to capture Canada from the French. They were pretty successful capturing Tadoussac at the mouth of the Saint Lawrence River, moved upriver to Quebec where after calling for the French colonists who were led by Samuel de Champlain to surrender they judged the defences too strong to force so moved back downriver, shortly before a French supply convoy arrived which they were able to capture in what became known as the Action of 17 July 1628 that netted them a large amount of plunder. Having weakened Quebec by depriving them of supplies and reinforcements the Kirkes sailed back to England to provision and plan for a return the following year. Having struggled through the previous winter the French colonists had no real choice when they were once again asked to surrender in 1629. All of the French residents were then shipped back to France.
The kicker however was that the surrender had taken place three months after the Treaty of Suza between England and France which ended the war by agreeing uti possidetis, both sides keeping what territory they had conquered, and reconfirming between Charles and Louis' sister Henriette Marie. This meant that the English would have to return Quebec. They weren't too thrilled about the idea but Champlain back in France kept pressuring the government to regain his territory and it was finally agreed with the Treaty of Saint-Germain-en-Laye 1632. So what happens if the Kirkes decide to launch an attack during their first foray to Quebec in 1628 and capture it? Champlain's refusal had been a massive bluff - the French were few in numbers, already short of food, had little in the way of gunpowder, even less of fuses and other supplies, and he generally thought that if they had attacked he was unlikely to be able to resist them. So for whatever reason Kirke decides to call his bluff and succeeds.
The most obvious is that France is no longer entitled to reclaim Tadoussac and Quebec back. These are the only two settlements in New France on the mainland at the time as they don't appear to have built any of the later forts around the Greats Lakes or the lakes further west in what would become Manitoba. The only other one was Port-Royal in Acadia in modern day Nova Scotia. Aside from this one island the French have just been kicked out of North America.
Do the French still try to colonise along the Mississippi? In our timeline they explored it coming down from the north which is now out of the question. The mouth of the Mississippi had already been discovered around 90 years beforehand, do they try and come up from the south or do they simply decide to write things off and concentrate on other areas such as the Caribbean? The French did try and colonise what's nowadays Texas in the late 1600s and whilst the Spanish owned Florida they don't seem to have made much in the way of effort to expand westwards so there's an opening. Whether they do it without the northern end to link up with is the question. If they French don't then the most logical alternative is that the Spanish slowly expand along the coast I would think, or some enterprising colonists from another nation could try jumping in. If they don't then where do they expend the extra resources that this frees up? The Caribbean and possibly India seem to be good candidates.
What does this do for relations between the English government and future American colonists? Aside from the Dutch and Swedes who can be taken care off much more easily the only other threats are the Indians, who here the tribes don't have the a European alternative to play off against the English, and the Spanish down in Florida. One major benefit will likely be French Acadia being captured fairly quickly the next war, the Nine Years' War if things don't change too much, and not given back so no incidents of the colonists fighting to capture territory only to see it traded back in the peace negotiations in Europe. A much reduced need for military protection means much reduced expenses so likely fewer taxes needed to pay for them. No Quebec means no Quebec Act which angered them by both allowing them to remain Catholics and also expanding Quebec south into the Ohio territory blocking land the colonists wanted themselves. The reduced threat however could also potentially encourage them to feel that they don't need England's protection and strike out for themselves.
These are all random ideas so far so any suggestions people can make would be welcome. Going to have to sit down and think things through since there are a whole host of possible knock-on effects and butterflies.
Edit: I got my Latin mixed up, wrote status quo ante bellum instead of uti possidetis as I meant to.