England gets invaded by the Spanish Armada, becomes a decentralized mess of nobles and bishoprics, etc and never becomes a contender in the colonial game. By dominating the London market, Dutch trading companies become the leading force behind settlement of the Eastern Seaboard. Swedish and Finnish affiliates of the Dutch interests in the Baltic become involved in the fur trade network, and their cultural impact filters across the Hudson Bay and Hudson River Valley. "Christianized" natives are taught Swedish or Dutch, and settlements of Swedish-speaking mixed race trappers pop up throughout the Hudson Bay watershed.
When push comes to shove between the various countries behind fur trade in North America (probably France, maybe a little more Spanish involvement with Britain not existing), it is from here that the victors will be: Swedish colonial forces from within the Dutch/Scandinavian company alliance. They will replace French culture in the main cities with Swedish culture to the extent they can, at best it'll only ever be a plurality.
More of the hither regions will be Swedish (or the quasi-Swedish settler culture that's developed) almost exclusively, augmented by an extensive "Blandat" (Swedish for mixed race) culture that dominates places like Northern Quebec (Nord-du-Quebec in OTL) which even in OTL are majority First Nations demographically. Swedish will effectively be the lingua franca for much of North America north of the Great Lakes and Mississippi watershed, much like Canadian borders OTL. It might even supplant settlement from other nations in the Great Lakes and gain territory and settlement rights to both Peninsulas in Michigan and Wisconsin and Minnesota, basically the upper Midwest.
Interestingly enough, regardless of borders, if one speaks Swedish ITTL, you could easily travel from Yukon to Greenland to Newfoundland to Ontario area... You get the idea.