A drive by President François Hollande to legalise gay marriage is shaping up as an epic battle between left and right but also between urban France and "La France Profonde".

The leader of the main centre-right opposition party, Jean-François Copé, provoked a storm of criticism yesterday when he called for street demonstrations against all left-wing projects which threaten the "pillars of our society".

He suggested that if he won the battle for the party presidency next month he would call right-wing voters to stage mass protests to protect "the future of French children". He gave as his model the large right-wing demonstrations which protested – successfully – against the abolition of Catholic schools in 1984.

Separately, rural politicians – not all of them on the right – are campaigning for "a conscience clause" which would allow the mayors of villages and small towns to refuse to perform same-sex marriages when they become legal, as expected, early next year.

Mr Hollande made gay marriage one of the planks of his presidential platform in the spring. The issue has turned into a potential political minefield for both government and opposition. Homosexuality is broadly accepted in urban France but prejudice is still rife in rural areas and on the Catholic and conservative right. A draft law is expected to go before the government next week to amend the Civil Code – civil and family laws dating back to the Emperor Napoleon – to allow marriages between same-sex couples. The law would also abolish "mother" and "father" as legal terms in France and recognise only "parents".

The proposed law has also provoked arguments on the left over how far the French state should encourage or assist married homosexual couples to produce or adopt children. This dispute – and a possible challenge from France's constitutional watchdog – persuaded Mr Hollande to postpone a first cabinet examination of the law.

A first reading in the National Assembly has also been postponed from December to some time in the new year. It is now anticipated that the law will give gay couples equal rights to adopt children. It will not – as some gay campaigners had demanded – offer free medical aid to lesbian couples who wish to have babies by artificial insemination.

Centre-right and right-wing opposition has focused mostly on these "family" implications of the law, rather than the principle of gay marriage as such. Most leaders of the main opposition party, the Union pour un Mouvement Populaire (UMP), are anxious to avoid seeming viscerally anti-gay, which could damage their election prospects.

But not all UMP politicians are so cautious. The mayor of the eighth arrondissement of Paris, François Lebel – the man who officiated at the wedding of Nicolas Sarkozy and Carla Bruni in February 2008 – said in his town hall newsletter this month that gay marriage could lead to the legalisation of paedophilia, polygamy and incest.