There is also disagreement about the conduct of demonstrators and the police operation to contain them. Six people are now in police custody, after 98 were arrested last night, following angry clashes, during which police used teargas.
Amid claims that right-wing extremists infiltrated the march or that children in pushchairs were affected by teargas, tempers are running high.
What is clear is that in France, opposition to gay marriage is not dying down. A bill opening up marriage to homosexual couples was passed in the French lower house of parliament in February, and the Senate is due to begin examining the text on 4 April.
French campaigners against gay marriage, which under French law would automatically include the right to adopt children, say they will oppose any such law all the way to the European Court of Human Rights.
Many outside France and even within, are puzzled by the level of passion the issue has stirred in the country.
Senior figures in the French Catholic Church have spoken out against gay marriage, but in a country where by law, religion and state must be kept separate, they are not actually running the campaign.
Organisers have anyway been active in also recruiting supporters from France’s Muslim and Jewish communities.
So why in France, where religious observation is relatively low, has the bill met much stiffer opposition than, for example, in very Catholic Portugal?
Although Socialist president François Hollande made clear in his election campaign that he was in favour of legalising gay marriage, there is now a widely-held view that he is pushing the gay marriage bill to boost his left-wing credentials, as the dire economic situation prevents him from delivering on some other election hopes.
Few doubt the commitment of his Justice Minister, Christiane Taubira, who earned huge admiration in parliament, even among opponents of the bill, for her passionate espousal of the law and her dedication during long all-night sittings in a draughty parliament building.
But many opponents of gay marriage and adoption are angry that such an important and probably irreversible change in family relationships, should be the subject, in their view, of political expediency. They want a referendum, insisting that although Hollande won the presidential election, it was not because of his backing for gay marriage. There does seem to be some confusion among the public over the issue: in France marriage would automatically include the right to adopt and yet surveys show a rise in support for gay marriage since January and a fall in support for gay adoption.
Many on the demonstration yesterday were angry over media coverage of their campaign and what they felt were attempts by journalists (perceived as overwhelmingly in favour of gay marriage) to portray them as intolerant and homophobic or to ignore them altogether.
Many genuinely worry about the possible unforeseen consequences for the institution of marriage and the welfare of children if such a law is passed, but gay marriage is also one of the issues around which a frustration and resentment at François Hollande has crystallised.
Right-wing commentator Ivan Rioufol, writing in France’s conservative newspaper, Le Figaro, two days before Sunday’s demonstration, hinted that the bubbling annoyance of this section of the population, was heading towards a “printemps français” a French version of the Arab Spring.
He was exaggerating of course. France is, after all, the birthplace of Human Rights and a democracy whose citizens freely chose François Hollande and his programme only last year.
But his point was that a silent majority in France has had enough. Although Hollande won the election, the combined votes for right-wing parties in the first round was greater than the combined total on the left.
This lies at the root of some of the problems in France today. Many on the right repeat stubbornly that a partisan press whipped up dislike for Nicolas Sarkozy and gave François Hollande an easy ride, and that Hollande’s resultant victory did not reflect the real mood of the French people.
Many on yesterday’s demonstration said they feel ignored, even despised, by the government which is busy pleasing symbolic or noisier minorities.
They note that earlier this month the government voted in favour of legislation which granted amnesty to people who smashed up property during the course of an industrial dispute.
At the first major show of force by anti-gay marriage on 13th January, participants held thousands of pink balloons. Yesterday the mood had hardened somewhat. One father at the demonstration declared “We are not here to fly pink balloons or dance on the pavements.”
“On 13th January we were neither counted nor listened to” Albéric Dumont, one of the organisers offered, by way of explanation.
There was a new development yesterday. Big names from the right-wing UMP, (Nicolas Sarkozy’s party) had called on demonstrators to widen their reach and turn the demo into a protest not just against gay marriage and adoption, but against François Hollande’s political leadership.
Many held signs with slogans such as “Sort out unemployment, not marriage”, but there are varying opinions over whether this was a good idea or not.
What is clear is that despite recent talk in some countries that the left-right divide is now obsolete, in France it appears to be deepening, on both economic and social questions.
Yet many have lost respect for France’s mainstream right-wing UMP party after a bitter public leadership battle which dominated news bulletins in November. There is a vicious atmosphere generally in political circles at the moment and since Thursday an open war between some politicians and judges, which has further contributed to the fevered climate.
But this is mirrored by an atmosphere of profound division within the wider country; where unemployment is at a 14-year high, businesses are struggling, taxes are rising and the government will soon be forced to cut public services.
The position of France’s far right National Front in all this is interesting. Marine Le Pen, daughter of Jean-Marie, has worked hard to repackage her party and try to divest it of its old image as an anti-Semitic, racist, homophobic outfit.
She has carefully avoided close association with the anti-gay marriage protests, leaving the mainstream rightwing UMP to take a prominent role.
So far it looks like she can nearly afford to do without this group of voters. In a bye election on Sunday night, the FN candidate came a very narrow second to the UMP candidate with a score hugely up on last June’s parliamentary election. The Socialist candidate was eliminated after the first round.
But even as the FN maintains it's cleaning up its act, French domestic intelligence services report an increase in the activities of other far-right, this time underground, movements.