I happen to go by the bookstore owned by a French guy who's kind of a specialist (of manga, really, but he knows his bédés quite well too) and I asked him.
He said both are true. There were a lot of American strips in pre-war publications for kids in France. That's how they got introduced to the medium, as a matter of fact. They were "pre super heroes", though. Buck Rogers and Tarzan were two of the very famous ones. It's these strips that were gradually eclipsed by the introduction of European characters by publications like Spirou.
The superheroes appeared on the scene only in the late thirties, Superman was pretty much the first one. They were introduced in France during Libération, by the American GIs (for the good reason that between their apparition and then, there was the war). They didn't have the success of the earlier strips except with Americanophiles, because of the success of the Franco-Belgian magazines, but Guillaume thinks it's probably more a question that the values/mentality of the post-war Superheroes (that pretty much reflected the parallel rise of the USA as a superpower) didn't find much echo in post-war francophone Europe.
Early on as a kid, I knew of Batman, because we had the TV series. It must have been known in France, as the dubbed version was done there. Later on we had The Hulk also as a TV series, which we hated. We were far more vaguely aware of Wonder Woman, but that series was not dubbed in French, and I doubt my mom would have let us watch it anyway (She kept a close eye on the American shows she let us watch through the 70s-80s. As a militant feminist, she found them retrograde and disapproved of many of them).
When we were a bit older, there was a series of superhero cartoons (I remember there was Spiderman, Hulk, Captain America on that show), so I have some awareness of them, but as most francophone children of my generation, our favourite shows were almost all anime, either the Japanese, and a bit later the Euro-Japanese series.
Robert-Louis wasn't sure about the extent of penetration of manga in Belgium itself (he's left France to come here around the time manga were becoming popular), but he thinks that you may be wrong. As far as he knows, they sell well there too, but maybe more like they do in Québec than like they do in France (where they're now considered a mainstream genre, like bédé. In Québec, it's still considered something of a sub-culture even though it's starting to show signs it might pass into mainstream culture).
Forget the USA, they're behind Europe and way behind France concerning the popularity of manga, and unlike in Europe, the market has been growing very slowly in the USA (and it's still very much a sub-culture). The Japanese refer to the phenomenon as "The French exception". Aside from Japan itself, France is their biggest market for manga, and about the only one in the West where Korean and Hong-Kong titles also sell. Beside France (with Belgique and Québec in tow), manga sell extremely well in Asia, then also in Spain and Germany, and Brazil. Only then comes the US market.
There are whole manga sub-genres very popular in France that are not even translated in any other language at this point (not even in Asia) or still extremely rare, like the more experimental ones, the more literary genres, the more "serious" adult or social drama genres, the slice-of-life genre, the manga mostly for girls, the historical mangas, the educative mangas. One of the most popular manga right now (and one that you could say is the closest to mainstream in Québec) is one that's mostly an excuse to educate people in oenology (and as Robert-Louis pointed out to me, the success of that one is a sure sign of how japanophile years of manga success have made the French. It's unusual that anything about wine from abroad has any success in France).
The success of manga R.-Louis told me probably comes from a mix of the decades of Franco-Belgian bédé preparing the ground (many genres in manga aren't so exotic when you're into bédé), and then there's the fact anime took francophonie by storm in the late 70s and through the 80s (the wave died in the 90s because of a cultural misunderstanding of a sort). After that anime got a bad rep and were pushed out of the air in France, and so from Belgique and Québec as there was no longer French dubbing. They returned, but not longer fully "mainstream" as they were in the 80s.
In the 80s, following the huge successs of the likes of Candy, Albator, Goldorak, Démétan and so on, the Belgian and French animation studios freaked out a little (because anime is much cheaper to produce and they could no longer compete). Their answer was to set up co-prods with Japanese studios, for anime that would often be in part scripted in Europe but designed and produced mosty in Japan... Among those, Caliméro, Belle et Sébastien, Heidi, Les Mystérieuses Cités d'Or, Le Petit Castor, Les Trois Mousquetaires, Les Misérables, Sherlock Hound etc. There's been a lot of them at some point, some of which were very succesful in Japan too. Then French TV execs got a bit overeager and started buying the wrong series, not fully grasping that there was a lot of anime designed for young adults and adults, while the Japanese studios that sold them didn't understand that in Europe, cartoons are for children and they would be shown to children. And so the more violent stuff ended up shown in children slots, and people started protesting against them (Ségolène Royal even wrote a pamphlet against anime), and anime lost popularity and the European studios turned elsewhere for co-prods (Québec, notably).
Where manga come into play is that some publishers (Glénat is an early one), knowing the ties between bédé albums and some of the cartoons, and noticing the emerging interest in manga (Akira was one of the first, and very succesful), smelled an opportunity and picked up the manga on which the more popular anime were based. That was a big success (especially that some of those were for girls - like Candy, and there wasn't a big offering in bédé for them). The French knew these characters, so the kids took manga in stride and the demand developped.
As for manga influence on bédé, R.-Louis said there's a whole genre of bédé in France and Belgium called "La Nouvelle Manga" (a reference to Nouvelle Vague). The characters are a mix of influences from classic Franco-Belgian bédé and manga style. The format and pacing are often closer to manga than bédé, with a continuous story volume to volume rather than the stand-alone episodes bédé is more used to. Some of those are published by the likes of Dargaud/Casterman/Dupuis and co (generally as albums), others are published by the now numerous manga publishers. A great deal of those, so far, are in the Fantasy/medieval fantasy genre. There's something called "American manga", but for the most part those aren't drawn by American artists. Most are works for which a US publisher hire Japanese/Korean/HK artists.
Another recent phenomenon is that the French publishers are commissioning original works by Japanese artists that they sell after to Japanese publishers (mostly to manga magazines). So far, it's been series by artists who work in fringe genres that have difficulties finding a publisher in Japan.