This question is so vast and far reaching that pin pointing a single cause behind France absolute decline against Germany is in my opinion impossible.
In many more ways than meet the eyes France and Germany are vastly different countries. A common way to describe France in climatic and geographical terms in French high school is to say "France is a sumary of Europe", don't laugh that's the expression one of my teachers used. In a way however this is true since you have everything from continental to oceanic to mediterranean climate zones in France. In the same vein, France is open to the North Sea, the Atlantic Ocean and the Mediterranean Sea all at the same time.
If we look at Germany on the other hand, Germany has none of France internal diversity, all of its major rivers are flowing north towards the North Sea and the Baltic, most of Germany climate could be classified as continental.
What I am getting at here, is that it is a lot harder for a polity like France to decide where to focus its own energies, as it has several possible areas in which it could expand or project power.
France tried to project power southwards in Italy during the 16th century, this policy failed and was instead replaced by a policy of projecting power north and east, thence the wars of Louis XIV and the Rhine borders pursued by the Revolution. At the same time, France actively tried to expand overseas but these efforts were half hearted in some cases, since especially in the 17th century continental wars absorbed most of France own energies and resources.
For Germany things are a lot simpler on the other hand, as it is easier to project power into a single direction without being distrated elsewhere. This is especially the case for the Navy, when France has to divide its fleets between the Atlantic and the Mediterranean. Germany can focus on the North Sea only, any assets on the Baltic being easy to transfer through thanks to the Kiel Canal.
Geography also favours Germany over France in a lot of respects. As I said in another thread, the "centre" of Europe has always been on an axis begining in the Low Countries and ending in Lombardy or Venice. This is essentially the Rhine/Elbe valley and thence the Alpine passes to northern Italy. This axis is a natural transport route from southern Europe to northern Europe.
France by comparison as never been the undisputed economic centre of Europe. The only time it nearly claimed the title was during the middle ages, at the times of the Champagne fairs before trade moved further east or took to the seas.
Paris has never been a centre of trade routes in the same way as Amsterdam, London or Frankfurt were and still are. Its geographic position is ideal, but only as far as northern France is concerned, which is why it was ideal as a capital. Early political centralisation meant that no city ever became a rival powerful enough to challenge it. The same thing happened in Britain as well, except during the Industrial Revolution were London was briefly challenged by northern cities. So in a way, yes Germany early divisions probably helped it in the very long run.
"Historical Errors" have also played a big part behind the divergence between Germany and France. The impact of the French Revolution on the country economy was terrible, especially in the western habours who traded with the sugar colonies and around whom buddying industries and manufactures were concentrated. The Revolution and Napoleon continental system destroyed them, forcing France to reorient her development eastwards instead of westwards.
The significant conservatism and reluctance to invest of both the French peseantry and aristocracy also played a part in reducing France's overall potential for growth and development. It took two centuries for the potato to be adopted in France for example and an equally long time for things like cloverfields and such to be implemented to raise livestock farming productivity.
For France to reach her potential and consequently become the centre of Europe. A POD during the Revolution if not the Middle Ages is needed in my opinion. More domestically focused risk taking governments in the modern times would help as well, but they will come too late to bridge the population gap.
Interesting books here are Fernand Braudel books, especially The Identity of France series.