Why did the government of France become the center of European absolutism and not Russia? Was it simply fate or were there other factors which could explain why the era became known as the Age of Louis XIV?
French influence was of course directly linked to France's robust and expanding economy. Part of the reason it became the center for Absolutism in Europe and not Russia (which is usually classed among the States of Europe, which it should not be) is the relative weak Russian influence upon Europe. Furthermore, there are enough cultural differences between all of Europe and Russia that Russia should be considered as a separate case in such comparisons. One other factor was that of religion. Both France and Russia ascribed to the hierarchy of political and religious structures, and both were in that sense absolutist; however, France was a Western Catholic country, which was more identifiable to the rest of Europe, unlike its Eastern Russian Orthodox counterpart.
One of the other reasons that Russia was somewhat of a sideline was the xenophobic nature of Russia herself. Russia has always been suspicious of her neighbors and of foreign interest and not necessarily interested in cultivating a reputation or a place in the world so long as she is secure. Though Russia has had her moments of imperialism and expansion, they do not occur on the same level or intensity as those of other European powers.
One reason was that Russia was so distant from western Europe and lacked easy access to the Atlantic ocean. It therefore lacked a strong navy and could not easily participate in the kind of colonization that helped feed the powers of western European nations. There were Russian autocrats (such as Catherine the Great and Peter the Great), but they could not easily project their power beyond their own borders.
Russia was too peripheral and too backwards. France, by contrast, was a leading country in Europe and had been for centuries. It is pretty hard for a second rate country that is way off on the outskirts of a region to be seen as the center of anything. France was much more impressive because of its high culture and great military strength so it came to be the center of absolutism in Europe.