I see Bordeaux and Nantes, but they are a short ways inland. The U.S. has several like New York, Boston, Miami, Charleston.
First because most cities in France are much smaller than cities in the US. Compare a list of French cities by population with the same for the US. There are 11 cities in the US bigger than the 2nd largest in France (Marseille at ~855,000) and 34 bigger than the 3rd largest (Lyon at ~500,000).
Second, it does have big Atlantic coastal cities... by French standards.
Nantes and Bordeaux are both definitely ports, they're just up large, navigable rivers. Bordeaux is up the Garonne River and Nantes is on the Loire. An oceanic port on a river is a great advantage for transportation inland, and by being far up river away from the coast they provide a sheltered harbor. Portland, Oregon is the same way, a major port located 70 miles up the Columbia River from the Pacific Ocean.
Finally, the Atlantic coast of France is about 3 times shorter than the Atlantic coast of the US. So there's less space for cities.
I'm going into speculation here, but geography may also play a part: it's possible the Atlantic coast of France contains less natural harbors than the US does, or the winds in the Bay of Biscay made it difficult to obtain landfall. I'd love for someone to address that.
But even with all that, France just isn't very Atlantic-centric and that's where it's history comes in. When cities in France were being founded there was nobody to trade with across the Atlantic. Gaul (what the Romans called the area) was conquered by the Romans in 51 BC and by the time Europeans started trading with America France had already established her cities for a thousand years.
Her oceanic trading partners would be to the north (Britain, Norway, Germany, Baltic States, Russia) or to the south (Italy, North Africa, Balkans, Ottoman Empire). Being a continental nation inland trading along rivers was more important. Of the 10 most populous cities in France, 5 are on inland rivers (Lille, Paris, Lyon, Toulouse, and Strasbourg), 3 are on the south coast (Nice, Montpellier, Marseille), and 2 are on the Atlantic (Bordeaux, Nantes).
Bordeaux and Nantes are major cities and their proximity to the Atlantic coast was key to their development so there is nothing unusual about France in this respect, it does have some major port cities on the Atlantic coast.
The question, then, is really one of local geography. Those cities are located a few tens of kilometres away from the actual coastline, mainly because they are much older than US cities. Estuaries were convenient places to build ports and it's only recently that ship size became an issue.
In fact, Saint-Nazaire, a port/city located near Nantes and very closely associated with it was developed in the 19th century specifically because it's closer to the open seas. You could look at Bremen/Bremerhaven for a somewhat related development in Germany and even Rotterdam, while it does reach all the way to Hoek-van-Holland actually has a center that's located some 40 km from the current coastline, with the most recent parts of the harbour extending ever further towards the sea. Hamburg is similar too.
Another question is why French Atlantic ports are relatively small (compare Le Havre and Dunkerque - Nantes and Bordeaux are even smaller - with Rotterdam, Hamburg or Antwerpen). Here the major factor is a lack of a good connections to a large hinterland, something French ports still suffer from (by contrast, Rotterdam is extremely well connected to the Ruhr area for example). It's not a coincidence that Marseille (at the end of the Rhone valley, a major transit axis) is the largest port in France and one of its largest cities too.
Cities in the USA were built quite recently. When the first cities were being founded, the major trading partners were Europe - all located East of the East coast.
Cities in France were built a long time ago. When the first cities were being founded, the French could.
Travel North and meet the English.
Travel East and meet Belgium, Germany, Switzerland and Italy.
Travel South and meet Spain and Africa.
It would be surprising if there were some of France's larger cities on the West.
As French ports were well established on the channel and Mediterranean a long time before there was any real trade across the Atlantic. The French population therefore lived close to these channel and Mediterranean ports.
So we then need to ask what is the benefit of a port on the Atlantic? The goods would still need to be transported to the population centres, over land transport is more expensive then leaving them on a ship for a short additional distance.
The additional distance by sea to get to a channel or Mediterranean port in France is not that great due to the Atlantic coast of France being times shorter than the Atlantic coast of the US.
So ports that could be crated cheaply on estuaries made sense for serving the population close to them, but it never made since for a great investment to create large ports to serve population in the rest of France.
The French population had already moved to cities before trade across the Atlantic become an issue and as shown above, there was little real benefit in them moving again. In the USA, there was no (white) population before the trade across the Atlantic started.
Short answer: There are few rivers in France flowing to the Atlantic in France, and few natural harbors on the Atlantic.
In the case of Bordeaux and Nantes, there are rivers that flow into inland waterways. These are technically not on the Atlantic, which is the point of part of your question.
In the case of America, there are several cities that are located either at the mouths of rivers or at excellent natural harbors. Boston and Miami are "harbor" cities. New York is at the junction of Hudson and East Rivers, Charleston at the junction of the Ashley and Cooper Rivers.
Remember as well that Viking raids were devastatingly common for several hundred years. Coastal towns and cities were hit especially hard in Northern Europe. This raiding dissuaded coastal settlement for several hundred years ~800-1100- the time period which saw Europe crawl out of the Dark Ages. Since there were no competent state-level actors to protect vulnerable communities, some were abandoned after being attacked rather than re-built.
As many others have noted, France's long history tended to point in all directions except west. Until the age of exploration- beginning in the middle of the 15th century- no one, France included, was sailing west. This is not to say, however, that the Atlantic wasn't an important economic resource. It just didn't require large port cities.
As mentioned by @Schwern, the treacherous conditions of the Bay of Biscay make the area difficult for even modern day shipping operations. I cite the recent trouble the car carrier Modern Express:
"Winds blow from America to Europe and the waves grow all the way as they travel from west to east," says Prof Adrian New, from the National Oceanography Centre.
"These swell waves can be felt in the Bay of Biscay if you're still in deep water 100 miles out. They then become shorter choppier waves when you hit the continental shelf."
Swell waves are long sloping waves that are around 20ft high, but high winds can make them both bigger and steeper. Gales are most likely in the bay from October through March.
Source: BBC, 1st Feb 2016