The French word we use isn't secularism but laïcité, and in the past few years what this word and concept actually means has been the matter of heated public debate and political opposition. However, to discuss those more-or-less recent events here would no doubt violate the '20-years rule' observed in /r/AskHistorians.

If you want to go a bit further back in time, you have to consider how the modern French nation-State was built.

Prior to the Revolution (started in 1789), the French monarch was Roi de droit divin: King by the will of God. That was of course the God of the Christians, and the kingdom's religion was roman catholicism. State and Religion were mixed as the King was head of both.

During the Revolution, on November 2nd 1789, the goods and possessions of the Church were confiscated by the revolutionnary State. Some were then given back in 1801 and 1813 under Napoléon Bonaparte's rule, in accordance with the terms of two successive Concordates with the Roman Church. During the 19th century, the monarchy was restored, but the Republicans in France always advocated against the Church; they were vindicative secularists. From their point of view religion had nothing to do with governance, and vice-versa.

The Third Republic was brought to life by the end of the Second Empire and the defeat against Prussia in 1870-71. For a few years things remained unclear but by 1879 the Republic was stable. The question of the Catholic Church remained unanswered until 1905 when the famous law separating Church from State was written. This 1905 law states that:

Art. 1 The Republic guarantees freedom of conscience and the free exercicse of any cult

Art. 2 The Republic acknowledges, pays for or subsidizes none of the cults

So there you have it. French laïcité supposedly means nothing is forbidden (as long as things remain legal), and the Republic is religion-blind.

As you can see, the whole history of the French State vs. Church relationships revolved around getting the roman catholic church out of the affairs of the State. Nowadays (and in recents events) the question revolves around the place of religion, especially Islam, in public areas and in public affairs.

I am happy to further discuss these recent matters with you in PM. I have my biases, I will tell you which they are, and I'll tell you all I know. But this cannot be done here under the 20 year rule.

There's a tendency, even amongst the French themselves, to explain this as a legacy of the French Revolution. There's something to this. The Declaration of the Rights of Man (1789) states, “No one may be disturbed on account of his opinions, even religious ones, as long as the manifestation of such opinions does not interfere with the established Law and Order,” but the state and the Catholic church were intertwined pretty soon after (Napoleon's Concordant in 1801). Historians like John Bowen argue that it's roots are actually in the early years of the Third Republic, which used the concept of secularization (laïcité) of the state. This process of secularization was embodied in the 1905 law governing the separation of church and state.

Of course, the United States also has the separation of church and state, so it's fair to ask why the French experience is so different. The French Constitution (1958 ed.) states, “France shall be an indivisible, secular, democratic and social Republic..." which, at least on paper, resolves the "Are we a Christian nation?" question the United States wrestles with on occasion. The goal of the French approach to the separation of church and state is the desecularization of the public sphere, which is quite different than the American idea of public expression without the government picking favorites or interfering with said expression.

Being religious in France (and by religious, I'm largely talking about being Catholic) isn't a problem for a politician. France has a number of holidays based on the Christian calendar (Christmas, Easter Monday, Assumption Day, Whit Monday), so the cultural rhythms in France are familiar to Christians to some degree. Mixing your religious beliefs with your political platforms, however, is seen as a bridge too far. The Christian Democratic Party in France holds positions (it's against abortion and gay marriage) familiar to folks in the United States. However, it's leader was fined for saying homosexuality is an abomination and it's a non-factor in elections.

I can't speak to recent events without breaking the 20-Year Rule, but I will note that there were a number of controversies in France concerning headscarves in 1989 and 1994. Bowen notes that these fights are not over religion broadly--France went to pains to differentiate between "obvious" religious apparel like a headscarf and "discreet" apparel like a small crucifix on a necklace--but about the culturally-specific anxiety that certain symbols of certain religions caused.