This line in the lyrics was also very intriguing to me.
After checking the lyrics, I now understand this as referring to kids having been sucking their thumb for such a long time (waiting for their dad) that they have had enough time to - literally - eat their own fingers - all of them!
I would not promise I'm right here, but that's how I understand this.
The lyrics are the following: Faut l'sucer d'son pouce ou quoi ?
Dites-nous où c'est caché, ça doit
Faire au moins mille fois qu'on a, bouffé nos doigts
Therefore I also think that it means that you sucked so much your thumb that you end up eating all fingers.