Tens of thousands of people marched in Paris and Lyon on Sunday against new laws easing abortion restrictions and legalizing gay marriage, accusing French President Francois Hollande's government of "family phobia".

Marching in the French capital, Philippe Blin, a pastor from nearby Sevres, said he felt a "relentlessness against the family" in France.

Police said 80,000 people took to the streets in Paris, far lower than the organizers' own turnout figure of half a million.

At least 20,000 rallied in south-central Lyon, many of them ferried in aboard around 60 buses, waving placards reading "Mom and Dad, There's Nothing Better for a Child" and "Two Fathers, Two Mothers, Children With No Bearings" -- a slogan that rhymes in French.

The president of the lead organizing movement LMPT (Protest for Everyone), Ludovine de la Rochere, said she was thrilled with the turnout and appealed to the government to respond to the marchers' concerns.

The mass protest comes a week after several thousand people marched through Paris in a "Day of Anger" against Hollande's Socialist government, with the demonstration ending in clashes between police and protesters.

Those demonstrators railed against a slew of policies under Hollande — the most unpopular French president of modern times — including last year's law allowing gay marriage.

Other targets of LMPT's protests include medically assisted procreation (MAP) techniques for lesbian couples and in vitro fertilization (IVF).

They are also demanding the scrapping of an experimental school program aimed at combating gender stereotypes.

On Sunday, a few counter-demonstrators waved signs behind De la Rochere as she gave a stand-up television interview, one reading: "Protect Our Children from the Witches".