I assume this is what it's referring to: it's an allowance you get for your schoolkids at the "rentrée" (in September when school starts again) when your income is not very high.
"ALLOCATION DE RENTRÉE SCOLAIRE
Vous avez au moins un enfant âgé de 6 à 18 ans.
Cet enfant est à votre charge, vos ressources ne dépassent pas certaines limites.
Vous avez peut-être droit à l'Allocation de Rentrée Scolaire."
http://www.caf.fr/cataloguears/bas.htm
I think the "à raison du simple plafond" is a slightly contorted way of saying that the allowance is simply linked to your income level, you could maybe just say "income-related allowance" and not worry about the "plafond" element...If you do want to include it, I'd use "(income) threshold".