Vaudrait is the conditional form of the verb valoir, meaning "to be worth". It's a less common verb than many others, making it stand out.
In the song, the narrator's friend tells her, "Que sans moi, sa vie ne vaudrait plus la peine" (That without me, his life wouldn't be worth the trouble). This expresses a strong sentiment of dependency and emotional value, highlighting the dramatic stakes of the song's narrative.
Françoise Hardy's "Ton Meilleur Ami" [Your Best Friend] tells a really interesting story about a love triangle, or maybe just a very persistent friend! The singer is confused because her boyfriend's best friend keeps coming to see her and calling her every night. He even tells her he loves her, saying, "Que sans moi, sa vie ne vaudrait plus la peine" [that without me, his life wouldn't be worth living].
What's even stranger is that when she asks him why she hasn't heard from her actual boyfriend, he just repeats that he loves her! But our singer isn't having it. She doesn't want to believe her boyfriend would be okay with this. Eventually, she tells the best friend that he's wasting his time, declaring, "J'ai dit que je t'aime, Que sans toi, ma vie ne vaudrait plus la peine" [I said that I love you, that without you, my life wouldn't be worth living] – directly quoting the best friend's own words back to him, but about her true love. It's a pretty bold move!