When referring to possession in French, we use possessive determiners.
For example:
'mon livre' (my book). We use 'mon', because the word 'livre' is masculine.
'mon père' (my father). We use 'mon', because the word 'père' is masculine.
'ma voiture' (my car). We use 'ma', because the word 'voiture' is feminine.
'ma mère' (my mother). We use 'ma', because the word 'mère' is feminine.
This means that possessive determiners are never gendered according to the 'owner', but according to the noun itself.
Nouns in French - whether it's the name of a country, an object, or an abstract concept - are gendered. Therefore a woman talking about her book will say 'mon livre', because the rule of agreement does not take her gender into account, but rather that of the book, which happens to be in her possession and is masculine.
I was explaining this point recently to a new student who, first, looked baffled, as all English-speaking students do initially, because in English, we say 'her book'. Since nouns are not gendered, it's the gender of the 'owner', which is taken into account.
I quickly pointed out that it's the opposite logic in French and advised my student to remember such a 'paradox' and to be mindful of those determiners, rather than to agonise over the gender of nouns, which is arbitrary.
And, as I was introducing the plural versions of possessive determiners 'notre' (our) and 'nos' (ours), he exclaimed 'as in the cathedral of Notre-Dame in Paris!'.
He knew the sight and its name, but he had never paid attention to its meaning. By noticing the language in use, he not only added a memorable context to the language point, but he also started looking at language learning in a new, proactive way.
Paradoxically enough, it's easy to use a language in theory, as we all did at school, and forget that it is alive and constantly evolving. And, crucially, that it is around us at all times.
Don't hesitate to send me your questions.