This is hard to explain in English, a language without grammatical gender, but essentially the problem is that French’s default neutral form is masculine and some women feel that this renders them invisible.
Various remedies have been proposed: using words like professeure for a female teacher, or a proposed inclusive writing system using dots in the middle of words to include both sexes (‘agriculteur·rice·s’ – a farmer, male or female).
Some people – and not just reactionary men – say this is a lot of fuss about nothing and certainly not a priority in the struggle for parity between the sexes.
But, in a way, language is the foundation of civilisation. It is what we use to think with and if the words in people’s heads discriminate against women it makes it easier for society as a whole to tolerate disparities.
Some people say women in France earn 16% less than men which means, effectively, they work for free for the last 39 days of the year. If a vocabulary change can redress that situation, it is a small price to pay.
Verbal tricks alone will not reform many machistes but the language must belong to everyone and not be a tool of inequality. It is good for all of us, whatever age or gender, to learn to consider our audience before we express our thoughts in public.
It must not be overlooked, however, that every language evolves according to need and usage, whatever politically correct regulations say. As French society becomes more inclusive in actuality, people will find their own ways to verbalise their identities and relationships.
The day when women are fairly treated without question it probably will not matter which words are used.