Foudroie is a powerful verb that literally means "to strike down with lightning", from the noun foudre (lightning).
In the song, the line "C'est ça l'amour, ça te foudroie" (That's love, it strikes you down) uses this word to describe the sudden, intense, and all-consuming feeling of falling in love. It's directly related to the famous French expression un coup de foudre, which is how you say "love at first sight".
This song is a huge, dramatic celebration of finding love in Paris. The singer starts by telling us she's been searching everywhere for love, singing every day while wandering the city's neighborhoods: "J'ai cherché ton amour / Dans tous les faubourgs" (I searched for your love / In all the suburbs). When she finds it, it's not a quiet feeling. She describes it as a force of nature, saying "C'est ça l'amour / Ça te foudroie" (That's love / It strikes you like lightning).
She then invites her love to join her and promises to announce their connection to everyone. She's not shy about it at all! She wants to tell men, women, and children, and put it in every song she writes. The song builds into this massive declaration that love is everywhere and that with it, "Tu ne seras jamais perdu" (You will never be lost). It's a powerful and very romantic pop-opera anthem.