But if America declares independence, isn't there a chance that France, traditionally Britain's rival, will want to take the land for itself?
- BNC
Perhaps, but its dependent on the PoD.
If it is during the English Civil War, France was also pretty busy fighting Spain. Also, in 1640s, 1650s, from the perspective of New France, New Netherlands might have been a higher priority target, to capture the other terminus of the fur trade and crush the Dutch-Iroquois coalition that faced the Franco-Algonquin coalition.
I suppose they could hold down independent English colonies with deployed troops and Amerindian auxiliaries, though it wouldn't be easy. French colonial population was small. Although New Netherlands could benefit from external (Dutch) support it could probably be kept under occupation more easily than New England, or possibly Virginia.
If America rebels in favor of William in 1688, but William loses in the British Isles to the Stuarts, the French might be interested in grabbing the English colonies on the seaboard for plantations and to eliminate an area allied with William and the Dutch. The Stuarts could be angry enough at New England to give the French carte blanche to conquer those colonies. However, by this point the English colonies would be even more populous and troublesome to occupy.
A cool scenario. What about the converse? A bunch of Royalists flee to the colonies and defeat the roundheads there?
This has been discussed before, with the consensus that it is largely unlikely. The King fleeing to America is much further from home and from help than if he's in France or elsewhere in Europe. By fleeing this far he's admitting he's not likely to come back, he's living in a rough frontier at a lower standard of living than if entertained by a European monarch and is still open to being overcome killed and captured by a revolt by colonists and a pursuing parliamentary army from Britain.
Do the same considerations apply in reverse? That is would fleeing parliamentarians in America be in danger of a pursuing royalist force? Perhaps, but there's a greater chance that roundhead types or other anti-Stuarts could better stomach living in the austere conditions of America.