What is France's traditional costume?

France does not really have one national costume.

There are many regional costumes, although not many or even non is/are still used as daily dress.

In the last half of the 20th century, the 'typical' French male item was a beret.
And it is still used as a cartoon image for the French.

If you are on the French coast you will likely also see a lot of striped shirts. I have never seen them inland and I have seen them on the coast of other European countries, but they do fit with the English 'French guy' image. (Results of image search here.)

It is likely as 'traditional' and 'national' as the poncho for Mexico.

As your question doesn't specify it has to be in France, you may want to try Little World Museum of Man, which is in near Nagoya, Japan. You can't purchase clothing, but you can wear clothing for a small fee. Look for "Alsace village" within the park. The women's dresses there are very similar to those for Alsace in Nic's answer. Even though the place may sound like a theme park, I was pleasantly surprised at how informative it was.

I don't have a clue as to whether France has national dresses, or mainly has regional dresses. I assume regional dresses are just as good as national dresses for your purposes.

As rather generic advice, rural areas or small towns and former colonies often keep more of a region or country's (or coloniser's) cultural heritage than the big cities. I suspect that the colonies in the Pacific are more likely to keep France's heritage than those in Africa, because the former may have less enmity towards France than the latter.

Some styles can be recognized as French, meaning that you can realistically expect some French people to sometimes wear it, and if anywhere in the world you meet someone wearing that then there is a slightly higher probability that they are French:

But such styles are not typically described as "traditional".

"Traditional" costumes exist, but they differ widely from a region to another, here are a few examples from various regions:

(Bretagne)
(New Caledonia)
(Basque)
(Alsace)
(etc)

As you can see, they have very little in common.