Tant pis is a classic French expression that means "too bad", "oh well", or "never mind". It is used to express resignation or acceptance of a disappointing situation.
In the song, the singer repeats "Tant pis, alors je reste avec toi ma chérie" (Too bad, so I'm staying with you my darling). He uses it to show he's settling for his current partner because the person he truly desires doesn't want him, perfectly capturing the song's bittersweet feeling.
This song is a brutally honest look at being someone's second choice. Stéphane sings from the perspective of a person who is in a relationship but is completely obsessed with someone else. They admit, "Je pense à elle, c'est nul" (I'm thinking of her, it sucks) and "Au fond de moi, je brule" (Deep inside, I'm burning). It's a classic love triangle, but with a twist.
The twist is that the person they actually want isn't interested at all. The reason given is almost comical: "Elle n'aime pas les blondes" (She doesn't like blondes). Because of this rejection, the singer decides to stay with their current partner. The chorus is a direct, and pretty cold, message to this partner: "Elle ne veut pas de moi / Tant pis, alors je reste / Avec toi ma chérie" (She doesn't want me / Too bad, so I'm staying / With you my darling). The song even includes a spoken-word part that sounds like the final rejection text, making it clear that staying with "ma chérie" is the consolation prize.