Since all the other comments have been deleted maybe I can try my hand:

The long and short of it is that any count of won/lost battles and wars would vary greatly based on how they're counted. If we look at Rome, for example. Are the three Punic Wars three wars or one? What about the Arab Wars between the Muslim Caliphate and the Roman Empire; how many wars were they? Do we count skirmishes during interbellum periods between wars as separate wars? Even battles have problems with how they could be counted. Many times the victor of a battle is uncertain. Napoleon's War/Wars are a great example of how arbitrary any count of won/lost wars/battles would be. How many "Napoleonic Wars" were there: one (from his rise to his death), two (from his rise to his capture and then from his escape to Waterloo), or more (his early Italian campaigns to his being crowned Emperor, his early wars to his capture, etc.)? Do his Russian campaigns count as a separate war? Does each time a small force of Russian raiders harried the retreating French force count as a whole battle? Even more problematic, where does France begin? Does the count of France's battles restart after the French Revolution? Do we start counting the victories of Frankish kings while part of France was still Roman Gaul?

So, while it's impossible to address the question directly, there is an implicit statement being made here. Modern viewers often view France as a paper tiger (this results from the beating it took during WWII). The statement posed in the original question is highlighting the fact that it isn't. That part is true. The best piece of evidence that I can put forward to redeem France's reputation is the fact that following Napoleon, France was considered so powerful that it took the combined weight of Austria, Britain, Prussia, and Russia to create a security arrangement that was considered to have put them at a parity with France (http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=461173&fileId=S0260210506007145 Sorry for the paywall. The article is also available on JSTOR, I think but I don't have access.). This is not to say that all of those powers couldn't have destroyed France if they wanted to join forces, rather that to create a stable balance of power, it took all of those states acting consciously and in concert to counteract France. There are other examples of French military acumen but I think that's the best.

The area that comprises France is rich and populous and has been for quite some time. The states/kingdoms/republics/empires (whether you count them as one continuity or not) that have occupied that space have been able to draw on those resources to their advantage in war (There is a reason that French was the common language, or lingua Franca if you'll pardon the play on words, of Europe; look at Peter Rickhard's A History of the French Language for more.). That's really the most blanket statement you can make to that effect. Going over each war and battle to create an arbitrary count would be missing the point.

TLDR: It's impossible to count how many battles a country has won or lost in the long term. Even so, France was pretty bad ass for a while.

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Can you provide a specific source for the claim that France has won more battles and wars than anyone else? Perhaps the issue is the definition of a battle or a war. The Battle of Leningrad lasted for two years- was that a single battle, or a series of battles?