Yes, it is possible. From my personal experience, it appeared a few years ago, mainly in young slang. I suspect that it comes from a further reversing of the older verlan meuf. It is still a bit connoted as slang, and petite amie and copine might be more suitable when talking to older people who might misunderstand it.

Traditionally, at least in France (but probably in other French-speaking countries as well), femme means wife, in the officially married sense. France is traditionally a Catholic country where all marriages are performed by the Catholic Church. The rise of secularism has switched the role of the Church to that of the state, with an state official pronouncing the couple married.

In the late 20th century, official marriages have become rarer, but not living together as a couple. So there are a lot more stable couples who aren’t married — what you might call common-law marriage, though the exact concept doesn’t exist in France (concubinage is broader).

The use of the word femme to mean effectively a common-law wife (and sometimes dually mari) has risen. I hear it used by couples in a stable commitment — almost always living together, potentially having children, and intending to remain together for the foreseeable future. I don’t hear it from young people, but rather from couples who have been together for several years and have reached a stable phase in their life. Usually couples do not use the word femme and mari if they have definite plans to marry; they might use fiancé(e) even if they have not undergone any betrothal ceremony, or stick with copain/copine.

The situation between men and women is not symmetric because femme doubles as meaning woman and wife. A woman can say mon homme, meaning “the man I’m in a stable relationship with”. This usage is older than the use of femme to mean “the woman I’m in a stable relationship with”. It doesn’t imply marriage or the absence of marriage. Due to the possibility of this alternate wording, using mari with no legal marriage is rarer than using femme (but not impossible).

When a couple uses mari/femme, there is an implication that they are a stable couple and that’s all you need to know about them: whether they have made an explicit legal commitment is family business that is not always aired to strangers. The use of mari/femme by unmarried couples is a minority usage, but a rising one. If you say “voici ma femme” and you fill in forms where you need to indicate your legal marital status, it may still raise eyebrows if you don’t tick the “married” box, but less so over time, especially now that intermediate status of PACS exists.

People who use the designations mari/femme tend to prefer them to copain/copine or petit(e) ami(e) because these other expressions do not convey stability. You have a copine or petite amie as a teenager or young adult (whether it’s for a month or a decade), but a femme as a mature adult in a long-term relationship. Increasingly, this is the difference, and not whether the relationship was made official.

In this particular context, I think it is the equivalent of calling a boyfriend “mon homme”, i.e. “my man”, which doesn’t suggest a marriage link in either language.

In this context (unmarried, expecting a child, looking forward marriage), femme is certainly used these days in France, and have been for more than 20 years now; it would probably be blonde in Quebec.

Copine is colloquial but could be also heard, particularly toward young people (below 35); it is somewhat less precise. Petite amie is also used. Both terms do not carry the same kind of relationship as femme however, they can also cover the case for the unstable, early days, where femme would not apply.

By the way I am unsure girlfriend would be the most used term in English in this context.

What is, in my experience, far more common, is the expression « homme » for “boyfriend.” A few years back, there was a radio talk-show host on the french radio station NRJ who went by the name T-miss. She would frequently refer to the female caller’s boyfriends as « ton homme. » To me it always felt a lot more charged than the mere « ton copain/petit copain/ami », and implied a more passionate relationship, one where a masculine principle and a feminie principle clashed in a unpredictable tempest of passion, though I may be the only one to feel this ^^.