Gavial refers to a gavial, a type of crocodilian with a long, slender snout. It's an unusual and specific animal reference, making it quite memorable and unique in a song.
In the lyrics, Gainsbourg describes Charlotte "à quatre pattes comme un petit gavial" (on all fours like a little gavial), creating a vivid and somewhat quirky image of a child. This unexpected comparison adds a touch of playful eccentricity to the song, characteristic of Gainsbourg's style.
Serge Gainsbourg wrote this one for his own daughter, and you can hear it the moment he calls her a little "Charlotte aux pommes" in "Tu es une petite Charlotte aux pommes" [You're a little apple-tart Charlotte], a pun only a dad allows himself. The whole song is built around one sound he keeps repeating to calm her down: "Shush, shush, shush Charlotte" [Hush, hush, hush Charlotte], said so many times it stops being a lyric and starts feeling like a habit.
What he's hushing gets bigger every verse. First it's a toddler thing, "Quand tu faisais poupou dans ta culotte je te disais" [When you were pooping in your pants I'd tell you]. Then it's a kid running late for school. Then it's a teenager losing her temper at cards and swearing exactly like her father: "Tu dis 'merde', 'chier', 'con', tu râles" [You say 'shit', 'damn it', 'idiot', you gripe]. By the last verse he's not calming down tantrums anymore. He tells her straight, in the gentlest voice he's got, "Sais-tu, ma petite fille, pour la vie il n'est pas d'antidote" [Do you know, my little girl, there's no antidote for life], that one night he won't be around, and he doesn't want her crying about it. Same three words cover all of it.