Oh wow, an alternate history where the Peace of Amiens is kept? Never thought of that *cough* Shameless Plug *cough*
But from my speculation, I believe France would, as many pointed out, begin strong in Europe in 1802. German nationalism I think, began truly as a result of Napoleon's invasion and the creation of the Confederation of the Rhine. Assuming this is all butterflied away, the Germans in the Rhine wouldn't mind living under French rule.
I believe the people there were largely Francophiles, and resisted Prussian rule IOTL. Perhaps once coal is discovered, Frenchmen migrate to the Rhineland and the working class there begin to slowly assimilate into French culture. They'd probably retain their own culture, but with the two mixing into a unique blend of the two.
Germany, if it is united ITTL, will probably have a rough time economically without the coal of the Rhine. Saxony might be an alternative for them, but I don't think it'd enough to compete with the Rhine.
I think France would be a strong nation for the rest of the 19th century, but would have to ensure no rivals take her place, probably like Britain fearing the German Empire overtaking her IOTL.