If I try to buy something in the ingame store I can put it in the cart but if I click the "pay in euro" button nothing happens. Problem exists since the fr3 update.
You need to have the Steam Overlay enabled. In steam, go to the top left and click "steam" then "settings" then "in-game" and select to enable the steam overlay. Then go in game and try. If that does not work, go to game.raceroom.com/store and log into your account there. It will just use your steam login which the game already uses and is connected to your profile. If either of these methods dont work, report back.
For curiosity sake, did you try enabling the steam overlay? Or did you go straight to the web store? Glad it worked though