This implies a major shift in the overall grand strategies of Prussia and France. Prussia's attempt to become a colonial power led to too many resources and attention being spent on New Prussia, all but directly leading to Prussia being partitioned. Prussia's conquest of Swedish Pomerania for superior Baltic control and its wars against Denmark to force Prussia's exception to the Sound Toll ended up pissing off both Sweden and Denmark-Norway, and its lack of focus on its army left it vulnerable to the PLC which attempted to use new conquests to halt its decline and the Hasburgs were looking for any opportunity to retake Silesia. Prussia's rise under Frederick the Great wasn't sustainable in the long term, but if it had focused on its army it might have survived as a medium German power like Bavaria or Saxony. New Prussia even with all this only survived due to the numerous refugees that came to New Prussia after Prussia's fall.
Meanwhile France never quite got into the colonial game besides several high profit areas like Caribbean sugar islands, India, etc. It instead focused on gaining dominance in mainland Europe.
The more possessions France has in colonies, the more focus it places on its fleet and overseas ventures. This would naturally come at some cost to its position in mainland Europe. Meanwhile a Prussia without New Prussia to funnel men and resources to will likely have more success domestically and against its neighbors.
OOC: Assuming Prussia preempted French Louisiana entirely rather than somehow taking it over, would a POD in 1682 really still allow the 'United States'? Not quite sure where the POD should be. Seven Years War?
Prussia had always been considered a powerful German state primarily due to its "Mercenary Powers": namely, Fredrick's doctrine of selling its crack-drilled army's services in exchange for wrangling political concessions from its rival. However, it barely had the economic base to sustain that over the long term, particular as route drill started to give way to flexable tactics, heavy compliments of artillery, and larger subject-soldier forces over smaller professional bodies. P-L and the kingdoms of Scandinavia always had her outclassed in terms of their population base and economic-manufacturing might, so even if she haden't diverted her funds to New Prussia I doubt she'd be able to continue at her pre-Conquest levels indefinately. Decades before her famed military was little more than a museum peace who, while of high quality in the type of warfare it was trained for, was stocked with museum peaces she coulden't afford to replace.
Perhaps the money saved by not building up a navy though could be funneled into a larger compliment of land artillery though, if she could get over her national pride and adopt the post-Fredrickian mindset of Napolyon Pasha. Even that's pretty unlikely though given how much of their identity was wrapped up in their strong domestic military tradition: more than likely the Kings would just invest in more and more soldiers and rifles, which dosen't do much to expand their tactical options.
The biggest change, though, is quite likely the butterflying away of
La Valse Sanglante that defined the politics and conflicts in the Germanies and Italies for nearly a century. If France is expanding in the Americas, that's naturally going to put her at longerheads with Great Britain, Spain, and the Dutch, which would really limit the amount of attention she could pay to her eastern frontier. Without that expansion into and develop of economic and political ties with centeral Europe, I doubt her rivalries with P-L or the Hapsburgs would develop into anything remotely like they did in our timeline, which wipes out the various Wars of Succession and proxy conflicts between princelings those powers used to try to undermine one another. And if Poland and Austria have their attentions turns south and east rather than west, they may very well be able to put enough pressure on the Ottomans and Swedish Empire to limit their rise to power. So many potential changes... you could write a dozen timelines on this.