France's government is facing trouble with its hopes to promote gender equality in schools and give unmarried or same-sex couples with children similar rights as married ones.

President Francois Hollande's Socialists have run into unexpectedly strong pressure from an alliance of conservative Catholics, Muslims and the political right over a landmark reform of family rights law.

The divisions have even seeped into the ruling party, which is already facing criticism about its handling of the lackluster French economy.

Prime Minister Jean-Marc Ayrault this week shelved the plan indefinitely after tens of thousands of demonstrators protested against what they called France's "family-phobic" government. The government retorted it had already planned to delay proposals to increase access to in vitro fertilization and redefine custody rights and adoption law.