I think it has to do with the terrible grammar education in English (it’s useless to teach about split infinitive when nobody can tell what an infinitive even is!). In my experience, genuine grammatical education is far more prominent in French-speaking countries (whether it is actually effective is another issue entirely). Generally, punctuation is significantly “better formalized” in French (punctuation “advice” in English tends to be little more than a pile of half-useless bugaboos and peeves.).

It’s also useful to not that compared to two centuries ago, current literature in either languages uses a lot less commas in general.

I’ve performed a small experiment for you, finding commas per word in French and English texts. View this as anecdotal evidence, not data, since I’m using a sample size of two: Voltaire’s original “Le Blanc et le Noir” and the English translation, and the Universal Declaration of Human Rights (UDHR) in both languages.

Le Blanc et le Noir: English: 0.085, French: 0.082.

UDHR: English: 0.0517, French: 0.0532.

The number of commas per word in English and French is roughly equal based on these two texts. For a more robust answer, you’ll have to use a larger corpus made of non-translations (as parallel translations may bias the results to have a similar number of commas).

Methods used:

Le Blanc et le Noir:
Words per text:

$ wc -w english.txt 
5207 english.txt
$ wc -w french.txt 
4665 french.txt

Commas per text:

$ tr -dc ',' < french.txt | wc -c
383
$ tr -dc ',' < english.txt | wc -c
440

UDHR:

 udhr.raw('French_Francais-Latin1').count(',') / len(udhr.words('French_Francais-Latin1'))
 0.0532
 udhr.raw('English-Latin1').count(',') / len(udhr.words('English-Latin1'))
 0.0517

I have the opposite feeling. But it is only a feeling. One of the reasons that explain my feeling is that English sentences are generally shorter and English will have several sentences where French will have subordinate clauses that in practise entails the use of commas.
I expect that to go beyond a mere feeling we’d have to work on comparative studies in translation theory. There must be lots of academic stuff on the subject. Google shows about Approche interlinguistique de la ponctuation français-anglais, par Claude Demanuelli (1998), an extract (pp 45 to 49) on the use of the comma in French and in English is available through google books.

For rules and references:

About the use of the comma in French:
Lexique des règles typographiques en usage à l’imprimerie nationale :
La virgule sépare sujets, compléments, épithètes, attributs et propositions de même nature ou non unis par une conjonction de coordination. Elle isole les mots formant répétition ou mis en apostrophe, les propositions relatives explicatives. On ne séparera pas de leur verbe par une virgule plusieurs sujets, coordonnés ou non, de même que le verbe du complément d’objet, direct ou indirect. Deux « ni» peu éloignés l’un de l’autre ne doivent pas être séparés par une virgule. On ne mettra pas de virgule avant une parenthèse, un tiret ou un crochet, à moins que le crochet annonce une restitution. On fera précéder « etc. » d’une virgule.

On the web:
– A course of French as a foreign language, with a pdf file.
– Le site la-ponctuation.com.

About the use of the comma in English
The Chicago Manual of Style says:

The comma, perhaps the most versatile of the punctuation marks, indicates the smallest interruption in continuity of thought or sentence structure. There are a few rules governing its use that have become almost obligatory. Aside from these, the use of the comma is mainly a matter of good judgment, with ease of reading the end in view.

In my opinion the same could be said about the use of the comma in French. I’ve tried to translate the sentence into French and I have ended up with the same number of commas:
« La virgule, qui est certainement le signe de ponctuation le plus polyvalent, marque la coupure minimale dans la continuité de la pensée ou la construction d’une phrase. Il y a bien quelques règles qui régissent son usage et qui sont devenues obligatoires, mais en dehors de ça, c’est une question de jugement de façon à obtenir un texte qui soit facilement compréhensible. »

On the web:
– Rules for Comma Usage in the Guide to Grammar and Writing.
– The EFL site EnglishClub.com. (And that reminds me of the different use of the comma in French and English where numbers are concerned, but that is not what you were asking for in your question).

The Chicago Manual of Style is not freely accessible online but its Q&A part is, and has questions about the use of the comma.