I have been taught, that after the French revolution, the new French state took a lot of action to decrease the influence of Catholic church without trying to put any other religion in power.
Is there any state that have done that before : fight against religion not against specific religions in the name of one other, but against all religion ion the name of a religion-less state?
This isn't an answer to your question, but I have to point out that you've been taught bad history. The first French republic was absolutely not an atheist state. There was a strong atheist movement, but they were never in charge of the national government. The National Convention adopted a decree in 1794 announcing that "the French people recognizes the existence of the supreme being and the immortality of the soul". The same decree established an official way of worshiping the supreme being, and the supreme being is God by another name.