Data on the cost of the Quebec system has always shown that most children are not in the system, that cost are very high, and that increased taxes paid by mothers spending more time at jobs do not come near to covering the costs. See some cost data on pages 22 and 48 of this paper.
March 2005. LeFebvre, Pierre & Merrigan, Phillip. Centre Interuniversitaire sur le Risque, les Politiques Économiques et l’Emploi (CIRPÉE) – (report): “Low-fee ($5/day/child) regulated child care policy and the labour supply of mothers with young children: A natural experiment from Canada“