David Cameron is not the only European leader to be unsettled by the gay marriage debate. The French president, François Hollande, is under fire for his proposals to legalise gay marriage, as street demonstrations illustrate the deep divisions in society. Religious groups and the right have led thousands in protest rallies, while equality campaigners and several leftwing MPs have warned that the law will be shamefully inadequate in not allowing equal gay parenting rights or medically assisted procreation.

The Socialist president had hoped that the gay marriage bill, to be debated in parliament in January, would be a milestone in social progress: a key reform with his name on it, to detract from the negative headlines about the financial crisis. But French society is tearing itself apart over the issue with an intensity that was not anticipated by the government, and Hollande has been accused of not taking a strong enough stand to force full equality on to the French statute book.

While the UK law aims to legalise gay marriage in line with existing rights for British gay couples – such as adoption, assisted procreation and automatic joint parenting rights – in France the scenario is very different. Hollande's law is not just about gay marriage but also adoption for gay couples, which is still illegal in France and remains controversial. The proposed law would only allow gay couples the right to adopt if they were married, not in a civil partnership – a distinction that has rung alarm bells among equality groups.

The law would not give automatic joint parenting rights to gay couples who had a child together, nor would it allow medically assisted procreation or IVF. This would give French gay people far fewer rights than those in the UK, and leave a stark inequality between gay and straight couples which has infuriated many on the left.

Socialists and gay campaigners will take to the streets on Sunday for a demonstration which they hope will counter the outpouring of opposition to gay marriage and adoption from the right and certain key figures in the Roman Catholic church.

Last month, French activists from the Ukraine-based feminist group Femen were attacked with pepper-spray, and hit and kicked by anti-gay-marriage protesters when they tried to disrupt a rightwing march in Paris. Hollande was forced to calm furious gay rights groups after he told mayors they could have a "freedom of conscience" clause allowing them to opt out of performing same-sex marriage ceremonies at town halls. After an outcry within his own leftwing ranks, Hollande backtracked and said his comments had been "inappropriate".

Elisabeth Ronzier, president of the group SOS Homophobie, said: "This is a historic moment because it's the first time a French government is moving towards more equal rights for gay couples and families. But we're not celebrating yet because the proposed law still doesn't give complete equality. We want equal rights to medically assisted procreation. We want legal rights for co-parents – that means full parental responsibility for people raising a child with their partner. We have urged the government not to bow to the pressure of the opposition against this law. We expected some to oppose it, but we've been shocked by the violence of the opposition – and the retrograde, cliche-ridden arguments bordering on insults."

Amantine Revol, deputy president of the association Les Enfants d'Arc en Ciel, for families with gay parents, said: "We're not talking about virtual kids, we're talking about perhaps hundreds of thousands of children currently being raised in gay families in France who need legal rights. What is being proposed is not enough – couples would have to marry before applying to adopt their own children, which could take years. Gay co-parents need immediate legal recognition and the automatic right to be named on a child's birth certificate."

Séverine Humbert, 30, an environmentalist, and Klervi le Mestre, 30, a teacher, are in a lesbian civil partnership. They have a daughter, Garance, aged three months, carried by Le Mestre. Because assisted conception by sperm donor is illegal for homosexual couples in France, they had to travel to Spain from their home in Perpignan to use anonymous sperm donation. Humbert said: "It's stressful having to do things on the sly, to go for ultrasounds and checks before conceiving when you can't give the full reason. The financial and psychological cost is high.

"We're accepted as a family everywhere in everyday life; now I just want to be automatically legally recognised as Garance's parent. Under the new law we would be forced to marry before a long adoption process that could take years. If a heterosexual married couple used an anonymous sperm donor, the husband could simply declare himself the father at the town hall and be put on the birth certificate, regardless of having no biological link. As the co-mother of a child, I just want that same right. It's a simple question of equality for all."

The history of gay marriage

Eleven countries have legalised gay marriage. In 2001, the Netherlands became the first, quickly followed by Belgium. In 2005, Canada and Spain followed, despite strong protest by the Roman Catholic church in Spain.

In November this year, Spain's highest court upheld the country's gay marriage law and rejected a long-running appeal by the rightwing People's party, which had argued that the constitution defined marriage as between a man and a woman. More than 21,000 same-sex couples have married in Spain since gay marriage became legal.

South Africa, determined to bury all forms of discrimination, had enshrined gay rights in its post-apartheid constitution in 1994. This led to it becoming the only African country to allow same-sex marriage in 2006, despite opposition from some religious and traditional leaders in a society that remains conservative on issues of sexuality.

Norway, Sweden, Iceland and, mostly recently, Denmark have also legalised gay marriage. Significantly, in what the Danish government called a "historic" vote, the parliament in Copenhagen made it mandatory for all churches to conduct gay marriages.

In 2010, Portugal followed Spain in legalising gay marriage. The same year, Argentina became the first Latin American country to allow same-sex marriage. In Mexico, a same-sex marriage law was enacted in 2010 but only in the capital, Mexico City. This month, the Mexican supreme court ruled that Oaxaca state had acted unconstitutionally in defining marriage as a legal union between a man and a woman. This could open the way for the eventual legalisation of gay marriage across Mexico, but it remains a lengthy legal process in each state.

This month, Uruguay moved closer to legalising gay marriage after the low house of congress approved a law that would make all marriages equal, regardless of the couple's genders. The bill must now pass through the senate.

In the US, marriage rights are defined on a state-by-state basis. In November, voters in Washington, Maryland and Maine became the first to approve gay marriage at the ballot box. They joined an list of states recognising same-sex unions, including New Hampshire, Iowa, Connecticut, Massachusetts, New Hampshire, New York and Vermont, as well as the District of Columbia. But 31 states have amended their constitutions to prohibit same-sex marriage, North Carolina most recently, in May.

This month the US supreme court announced it would take up the issue of same-sex marriage for the first time, agreeing to hear two cases that could decide whether gay and lesbian Americans have the same constitutional right to marry as heterosexuals.