There's quite a few things as to why France was a great power.

Location

The location of France is vital to it's survival. It was protected by the Pyrenees which divides France from Spain as both a physical and political border. This is also important because to the South, Spain was focused in a state of near constant war against Muslim forces, allowing Spain to grow while France was busy getting it's act together and expelling England.

To the South East is the Alps, another important physical feature that separates Italy (which was broken into city states and Habsburg lands) from France. Mountains are great physical protectors.

To the North East is two major protections, the Rhine and Netherlands. The Rhine is an important boundary that basically says French and German. East of the Rhine is German by culture and political dominance by the Holy Roman Empire. So it acts as a nice cultural boundary but also a political one that remains today.

Now the Netherlands is another thing that protects France by simply existing. The Netherlands is useful because at one time, it was a possession of the Habsburg family (mainly Habsburg Spain then given to the Austrian branch after the War of Austrian succession). I would argue that the existence of the Dutch Republic gave the French further time to get together and unify as the Spanish were busy spending a hundred years (between the 1580s till the 1680s) losing wars against the Dutch, those of whom would form the Dutch Republic.

Population

Due to the physical size of France, France enjoyed a rather large population advantage to the rest of Europe. If I recall correctly, at the time of the French Revolution, you could expect a population count to be around twenty to twenty two million at minimum. Compared to other countries (Britain was I think at about thirteen million at this time while Austria was around eighteen million), France enjoy more of an advantage in terms of using the population for economic gain. With millions of more people to gain taxes from, France could enjoy more economic freedom to tax.

Enemies

The oddest thing about the enemies of France is how unmatched they are. The Habsburgs were enemies of France only due to dynastic rivalry which came to a point during the War of the Spanish Succession when the French claimed Philip V of the House of Bourbon as the successor to the Spanish throne over the Habsburg's Charles III.

Aside from the Habsburgs, France's eternal rival was England/Britain, whom was a maritime power. France on the other end was a strong continental power that had one of the best armies in Europe. Britain knew it didn't have the manpower to commit to a continental attack while France never had the navy to really contend the British navy.

Culture

At a time, the world spoke French. This isn't due to the French aggressively expanding in every way, but rather due to how the French were able to successfully position themselves as culture. French became the court language of Europe. Frederick the Great and Catherine the Great (of Prussia and Russia respectively) spoke French primarily and up until the Russia Revolution, the Russian nobility spoke more French than Russian. If you read a Russian novel, you should expect a lot of French phrases, which shows the level of Frenchness that Russia had. I always enjoy pointing out that outside of France, the Russians spoke the most French in the world.

With French becoming the language of Europe, it also became the language of diplomacy and culture. So French came to become a power due to culture, not just success in war.

Victoire

While people may joke about the French as "Cheese Eating Surrender Monkeys", the French have one of the best records in war. The fact that France has existed with the shape it roughly has right now is a testament to it's skill in warfare and diplomacy.

During the time between the Seven Years War and the Revolutionary Wars, there were a lot of theoretical discussions on how the French should fight. This type of discussion and interest in how war should be waged differs greatly from the rest of Europe at this time, which kept the things that worked and had little interest in reform. Oddly, it was these ideas that were discussed before the Revolution that contributed to French victory throughout the Revolution and into the Napoleonic Wars.

Further, the French thought themselves as the bravest people in Europe. The French had elan while the rest of Europe lacked courage. This is seen in the French way of war during the Revolution, which was more focused the attack to the point that it almost became a cult that became abused during the Great War (when attacking entrenched positions was common). So, France was always on the attack, rather than on the defense.

Further, it learned from it's mistakes. The failure of the Seven Years War kick started a discussion of why France had lost and how it could have been fixed. This led to discussions on light infantry, massed artillery, the column versus the line, and the use of cavalry. It created it's own ideas rather than copy from Frederick, which most of Europe was doing at the time.

The Nation State

I add this only because France is very unique on these lines. In the political history of Europe, you will find five major powers; England/Britain, Brandenburg-Prussia, Habsburg Austria, Russia, and France. (You'll see others like Sweden, Poland-Lithuania, Spain, and the Ottomans, but they fizzle out by the 18th century, often at the expense of the major powers named). Of these, three exist right now along national conceptual lines while Prussia and Austria are shades of their former existences.

I'll rule out Russia because there is a larger history behind it's national history but Britain, France, and Spain had a concept of what they were as a nation long before the contemporary picture of Europe. A major part is the work that Louis XIV did in centralizing power in the King rather than having the old feudal system that had wrecked France during the 30 Years War and before. Due to centralization at Versailles and later in Paris during the Revolution, Paris became the main hub of French culture, which in turn turn France into a unified country due to a centralized political and cultural foundation.

Further, the Hundred Years War is another reason for unification. Geoffrey Parker argues that France had become the first nation state due to the fact that it had to unify to fight the English. By unifying, it had developed the seeds of the nation state by creating a single concept of "France" as the lands ruled by the French crown and only the French crown.

So France had a special strength in being centralized and it gave it power in every way that I mentioned before hand.

Conclusion

France is a unique creature; from the Hundred Years War, France was able to pull from a war torn country to a strong and centralized country that was able to further become a cultural and political power in all of Europe.

I hope I covered anything, I'll make a note if I forget something but this seems to be everything.

N. B. I must add a note that I am quite biased toward French history, so I ask that people whom disagree to say something so we can work it out.