To learn French with songs, take one song at a time. Read each line next to its translation, then loop it until you can sing it, and mark every place where the singer's French differs from the printed lyric. Those differences, like the apostrophes and the missing ne, are what French songs teach best. Some songs also teach a pronunciation nobody uses in conversation, so it pays to know which kind of song you're listening to.
Singing does help the words stick. In a 2014 study by Ludke, Ferreira and Overy, 60 adults spent 15 minutes learning Hungarian phrases by listening and repeating. The group that sang the phrases did better on the recall tests than the groups that spoke them or spoke them in rhythm. That was short-term memory for phrases, not fluency. But French has a specific problem that singing happens to target. Written French and spoken French drift a long way apart, and a song makes you hear the spoken version while you read the written one.
They drop letters you can see on the page. The e in je, de, le and me is the unstable vowel French grammars call the e muet or schwa, and its main trait is that it often isn't pronounced at all. Pop lyrics often print the drop with an apostrophe. Zaz's "Je veux" (2010) has "Je veux d'l'amour, d'la joie" (I want love, joy) and "C'n'est pas votre argent qui f'ra mon bonheur" (It's not your money that'll make me happy). Your textbook writes de l'amour, ce n'est pas and fera. On the radio you'll hear Zaz's version.
They glue words together. Liaison is the silent final consonant that comes back to life before a vowel. In Joe Dassin's "Les Champs-Élysées" (1969), "On a chanté, on a dansé" (We sang, we danced) comes out as on-na. The next line is "Et l'on n'a même pas pensé" (And we didn't even think). Say on a and on n'a out loud and you'll hear the trap: they sound identical, so the only signal that the line is negative is the pas. A song teaches you to wait for it.
They drop the ne. Your grammar book says negation is ne... pas. People speaking French leave out the ne much of the time, and William Ashby's recordings of speakers in Tours found young speakers dropping it more than older ones, with the habit growing between 1976 and 1995. Angèle's "Libre" (2021) is the best illustration I know, because it does both. "J'étais jamais devant" (I was never up front) and "Moi, j'oublie pas" (Me, I don't forget) leave the ne out. Then "J'suis libre et ça ne changera pas" (I'm free and that won't change) puts it back. Same singer, same song. That mix is how French sounds.
Older songs pronounce letters that speech drops. This is the one that trips learners up. French verse counts syllables, and in versification a word-final schwa before a consonant is pronounced. Wikipedia's example: une grande femme (a tall woman) is three syllables in speech and six in verse, u-ne gran-de fa-me. Sung poetry also uses every liaison that's allowed, including the optional ones casual speech skips. So when Édith Piaf sings "Quand il me prend dans ses bras" (When he takes me in his arms) in "La Vie en rose", me gets a full note of its own. In conversation it often shrinks to i'm prend. Copy chanson pronunciation into a conversation and you'll sound like you're reciting.
Rap and modern pop bring slang the textbook skips. The main one is verlan, slang made by swapping a word's syllables. The word verlan is itself l'envers (backwards) reversed. A few verlan words are now everyday French: meuf (woman, from femme), ouf (crazy, from fou), relou (annoying, from lourd), chelou (weird, from louche). Even Stromae's stage name is maestro in verlan. Learn that handful before you try French rap, or half the lines won't make sense even with a translation.
One song done properly beats ten you've half-heard. This is the order I'd use.
If you're still at the stage of picking a first song, our post on learning French with music covers choosing songs and building a listening habit.
All six have lessons in LyricFluent. I've picked them for what they show about French, not for difficulty.
Joe Dassin, "Les Champs-Élysées" (1969). A slow, clear chanson, and a French cover of the English song "Waterloo Road" sung by an American-born singer. Good for liaison, and for the on a and on n'a trap above. The chorus "Aux Champs-Élysées" repeats enough to learn by the second listen.
Édith Piaf, "La Vie en rose" (1947). Piaf wrote the lyrics, and she sings them with every schwa in place. Use it to hear the full written form of words like me and de, and to train your ear on the difference. Don't use it as a model for how to talk.
Zaz, "Je veux" (2010). Fast and full of dropped vowels, printed right in the lyric: d'l'amour, f'ra, "Moi j'veux crever la main sur le cœur" (Me, I want to die with my hand on my heart). It's a list of luxuries she turns down, so the vocabulary is concrete: une limousine, des bijoux, la Tour Eiffel.
Indila, "Dernière danse" (2013). Slow enough to follow, and the first French-language song to pass a billion YouTube views, so you've probably heard it. "Je ne suis qu'un être sans importance" (I'm just a being of no importance) keeps its ne and links un to être. Elsewhere, "Sans lui je suis un peu paro" (Without him I'm a bit paranoid) uses slang you won't find in a beginner's book.
Angèle, "Libre" (2021). The ne song from above. Angèle is Belgian, and the album it's on is called Nonante-Cinq, ninety-five, after her birth year. Belgians say nonante where the French say quatre-vingt-dix, which is worth knowing before you go to Brussels.
Stromae, "Papaoutai" (2013). The title is how "Papa, où t'es?" sounds: Dad, where are you? The chorus asks it in spoken French, with t'es for tu es and no inversion. Elsewhere it asks "Dis-moi où es-tu caché?" (Tell me, where are you hiding?) in the textbook form. Hearing both in one song shows you which one people actually use. It's a harder listen, fast and about an absent father.
Know which French a song is singing. Chanson gives you careful pronunciation with every schwa sung. Pop and rap give you French close to what you'll hear on the street. Learn from both, but don't mix them up. A full sung e in a café order sounds odd, and j'sais pas in a written exam costs marks.
Don't learn grammar rules from lyrics. Songs bend word order to fit a rhyme and drop words to fit a beat. If a construction looks strange, check it against a grammar before you start using it.
Expect regional French. Stromae and Angèle are both Belgian. Most of what they sing is standard French, but numbers like nonante and some vocabulary aren't what you'd hear in Paris.
Check the slang before you repeat it. Verlan and rap slang run from harmless to rude, and a translation doesn't always show which. Look a word up before you try it on a French speaker.
Don't stop at the chorus. Choruses are easy to learn because they repeat. The verses are where the new vocabulary is.