The French themselves generally regard '
frites' as Belgian.Their word frites is not a true French word.There is no verb in French for frying which is like 'frites'.The word derives from a Belgian whose surname was Frits. He was an entrepreneur who opened the first of what are called "
friteuses" , stalls selling chips (fries), in 1861. These were so popular that they were soon found all over Belgium and are still found to this day.His name seems to have been adopted for the product he sold. In France proper 'friteuse' is the word for the deep frying pan which is used for the frying of the potato pieces.It is this history that has French people thinking of the 'frites' as Belgian, it being the Belgians who popularised the dish.
A Belgian historian, Jo Gerard, has traced the chips to 1680 when they were cooked by poor people, when the local waters were frozen over, as a substitute for the small fish which they would otherwise eat but could not then obtain.This activity was confined to the area of the Meuse (a river) between Dinant and Liege. This is not as unlikely as it may seem. In Northern Europe, for example in Britain, 'chips' are made from thick long pieces of potato. Britons would not recognise what McDonalds cook,which McDonalds term 'fries', as 'chips'.
The area of the Meuse valley between Dinant and Liege is
now in Belgium. That's because Belgium did not exist as a country until 1831.

However in 1680 the area and the towns weren't French either but under Spanish rule, whilst technically part of the Holy Roman Empire and de facto independent of anyone

.So M. Gerard's discovery does not make the 'fries' French.
There is, incidentally, a very good reason why French cooks would not want to think of chips as French. The idea that anyone would want to cut potatoes into thick strips, strips as thick as a small fish, and fry them in deep animal fat would strike any purist as abhorrent! That's the kind of thing that makes Belgian 'cuisine' as bad as the old English cookery (which many would say it still is

)
In English we are quite free and easy in terming things as French.Why do Americans term fries 'French' ? We don't call them that in England, and never have it seems, though we do have 'French beans' which, coincidentally, are sliced thinly for cooking.
A common explanation is that 'to french' was once a cookery term for slicing food into thin slices for cooking: what French cooks call 'julienne'.If so this verb has not found its way into the current Shorter Oxford English Dictionary, which is not to say it was not once an American term or that it would not be found in the full 'Oxford' which contains many more words and includes some very obscure and obsolete ones.

If valid this might explain the thinness of American 'fries'
The French do sometimes lay claim to French fries. The problem here is that these did not appear there until the middle of the C19 when they were being sold by the Pont Neuf in Paris. These were thick, like the Belgian 'frites'. French chefs call thin fries 'pommes allumettes' ('matchstick potatoes') and used to call the Belgian type, the thick ones of 10mm or more thick (about half an inch upwards), 'pommes Pont Neuf'.
So it seems that the Belgians have it !
You may be met with a quote from de Tocqueville (?)about his country giving America various things including the fried potatoes. Well, what did he know of activities in 1680 in the Meuse valley?

PS Concerning frankvan's post above and my explanation about American soldiers: it seems plausible as an explanation for the dish being known as 'French' in America. It is certainly a version I've heard many times, though since giving it I've found a Belgian site which prefers the 'to french' explanation. Fries were not widely popular in the USA until post WW1 so it may be that Americans encountered them as a popular dish when they were serving in that war. The war itself was largely waged in north eastern France, the Belgian side. It would be naturalfor Belgian soldiers to prepare something as cheap and easy as frites, just like the ones found in Belgium.