Is it true that the majority of the French population today reports not belonging to any religion?

Yes. 53% of 18 to 49-year-olds gave that response  in 2019-2020. But this is a new finding: in 2008-2009 the corresponding figure was 45%. And if we consider specific groups within the general population, only 21% of immigrants, regardless of the foreign country they were born in, say they have no religion. Other differences are found within the immigrant group itself: the least religion-affiliated are Spanish immigrants, 42% of whom indicate belonging to no religion, while the most likely to say they belong to a religion are African immigrants, only 10% of whom indicate no religion.
However, French-born children of immigrants report more often than their parents not belonging to any religion (39% of them do so), though there is a considerable difference by whether one or both of the respondent’s parents were immigrants (54% in the first case, 23% for the second). In ten years, the proportion of people without a religion fell among those with no family history of migration (+12 points) while remaining stable for those with a family history of migration.
Although Catholicism is still the first religion in France (29% of the French population report being Catholic), Islam is the religion of an increasing number of believers (10%) and continues to be the country’s second religion. 

Source : L Drouhot, P Simon, V Tiberj, La diversité religieuse en France : transmissions intergénérationnelles et pratiques selon les origines, Insee références, Edition 2023 (chiffres issus de l’enquête Trajectoires et Origines 2 (Ined-Insee, 2019-2020).