I've thought more about this, and I think this applies not only to Atomic. I don't know if this is just my confirmation bias, but it seems that there is a link between the country of origin of a manufacturer and the nationalities of the athletes it sponsors. Probably this link goes both ways: manufacturers may be trying to sign best athletes from their home countries for the purposes of marketing, while athletes are likely to use skis from their "home" manufacturers growing up (more local reps, club sponsorships, etc.).
Of course, there are some exceptions, like Head, who are going after many top skiers (especially in speed disciplines), regardless of nationality: Norwegians (Jansrud and Svindal), Austrians (Maier late in his career, Mayer, Fenninger-Veith), American (Miller, Ligety), French (Pintu, Clarey), Swiss (Cuche), etc. But other than Head, I think the trend is pretty clear.
As
@Muleski said, top Austrians are almost always on Atomic (unless Head outbids them): Eberharter, Walchofer, Maier (most of his career), Raich, Scield, Zettel, Schwarz, Feller, Hirscher, etc. Well, not necessarily on Atomic-built skis/boots, but at least Atomic-branded. If they are neither on Head nor on Atomic, they are most likely on Fischer: Franz (he was on Atomic before), Schmidhofer, Siebenhofer, Kriechmayr (before he switched to Head), etc. I should note that Fischer is also actively involved in cross-country skiing and ski jumping, which may explain why their alpine budget may be somewhat limited and why they sometimes lose their top athletes.
There used to be Austrians on Blizzard, too: Hirscher early in his career and Mario Matt, but it seems that Blizzard has greatly reduced its involvement in racing. There are some Austrians on Salomon, but they are mostly lower-profile. One notable exception is Reichelt, but he is old and might have started using Salomon long time ago. Another notable name is Fritz Strobl, but it was long ago. Finally, there are some "odd" cases, like Liensberger and Michael Matt on Lange/Rossi, but they are very rare.
Next, as far as France goes, top French skiers are usually on French skis (unless they are on Head). Grange has been using Rossi for a long time (except for one season when he switched to Fischer), Worley has been on Rossi forever, Lizeroux was on Dynastar and then Salomon (with one season on Fischer in between), Muffat-Jeandet is on Salomon, Noel is on Dynastar. Even Pintu, who has been on Head for a while, started his career on Dynastar and then switched to Salomon, both French brands. In fact, while Rossi and Salomon have athletes from other countries, Dynastar almost exclusively focuses on the French skiers. One notable exception among the French was Thomas Fanara on Fischer. I can't remember anyone on Atomic, though: I would guess it is easier/better to give a French skier "French" skis (even if they are made in Austria) from the same "family" (Amer Sports).
Nordica has greatly reduced its World Cup presence, but its two top athletes are Italian: Paris and Vinatzer. As far as Völkl goes, I don't even know how to count them (Volklis a German brand, but Dalbello is Italian), but they sponsor relatively few athletes, too.
Overall, though, I think the picture is pretty clear: if there is a major brand/brands is a given country, a large number of athletes from that country is likely to be sponsored by it/them.
On a separate note, there are certainly interesting cases out there. Odermatt is on Stöckli skis (makes sense, as both are Swiss) but in Salomon boots. Not quite sure how his contract with Salomon works and why they are OK with supplying boots only. Liensberger wanted to use Kästle skis (again, makes sense, as both are Austrian) but wasn't allowed to. Luke Winters recently switched rom Rossi to Dynastar, which is somewhat unusual (I cannot think of many cases of switching from one brand within the same group to another). Finally, though Rossi and Lange boots are presumably identical, there are quite a few athletes on Rossi skis but in Lange boots. Presumably Rossi would want them to be in Rossi boots (as Rossignol is the "main" brand), but it does not happen. Liensberger and Michael Matt (already mentioned above), Brignone, Defago in the past.
Sorry if the post is too long... I just thought the link between the countries of athletes/manufacturers was worth emphasizing.