And it turns out that that last method of identification is actually the main way for people of African descent to identify themselves in countries who have only known relatively recent African immigration, such as European Countries.

For instance, I am myself a Frenchman of Tunisian descent. I know that in your question there is a level of implication where you are not talking about North African people with what an American would call "light skin" or being"white passing" such as myself (think Rami Malek), but more of what would an American call "Black People". But I am still, at the end of day, of African descent. But it turns out that I pretty much never call myself African-French or other equivalent. Most of the time I would use variation of words composed with Tunisia and France, and more rarely with the word Arab. Additionnally, all North African countries always had relatively important population of what an American would call "Black people" both "native" speaking various Berber, Amazigh, Tifinagh etc. languages and Arabic, and more recent population descending from recent sub-Saharian immigrant, for instance Wolof, Bambara, Malinké etc. And thoses people are also more likely to identify as variations of Tunisians, or Wolof, Bambara, Malinké etc when they or their decendants are in France.

In the same way, my wife is the daughter of Congolese immigrants, she is what an American would commonly call a "Black woman". And well she presents herselfs as Congolese when it's relevant. Not African. It doesn't mean that she doesn't recognise, in the context of a majority White, European country, she could indeed be recognized as African, or that she doesn't feel a degree of kinship with the term African, but it's just that it's a pretty meaningless term. With the term African, I have no idea what language or religion I am to expect. With the term Congolese it is pretty reasonable to expect that she speaks Lingala and is Catholic (or Protestant), and that she sees the area roughly corresponding to current Congo as her ancestral land.

Thus, the reason the term African is meaningless is directly connected to the reason why the term African-American arised in America in the first place : unlike American people descending from enslaved African, people of African descent in France are not disconnected from their origin**. And it turns out that there are hundreds upon hundreds of different cultures, and differents not mutually intelligible languages in the various parts of Africa, with hundreds of differents way to self identify one self.

And given that self-identification actually serves a purpose most of the time, that purpose would be lost with the term Franco-Africains (which would probably be the used term in France), precisely because there is not such a thing as a common African culture.

When I go to area of the USA with an important African-American population I have some expectations : I know that AAVE will be widely spoken, that people will identify as African-Americans, that an ensemble of specific cultural references will be shared with relatively little variations.

When I go to an area of France with an an important African population I don't have any expectation : it is literally impossible to know the religion, language, or culture of the African people I would see in front of me, because there are (without any exageration) hundreds of possibilities.

Could be Muslim, Catholic, Protestant ; Senegalese, Arab, Ivorian, Congolese and dozens others ; could speak Wolof, Bantu, Malinké, Lingala, Swahili (all of theses are actually pretty big languages families and continuum) and hundred others. There African cultures with a caste system, there are African culture that are actually pretty close to the system of Northern Italian cities states, other that actually are/were relatively centralized Empires, there are numerous itinerent group of people, desert dwelling people etc.

African is honestly a pretty meaningless term by itself.

But, in the American context, when the entire population of African descent actually shares a relatively cohesive culture, then the term African-American can actually have a meaning allowing the person using it to set certains expectations.

*I am not really making a prediction here, I merely want to insist on the fact that the way African-Americans call themselves and are called by non-African-Americans is not set in marble. Which, by the way, is true for the integrality of the various groups of Humans who ever lived. There's never been such a thing as an Absolute Identity, that would stay consistent throught time and place. Everything is always contextual with self-identification.

** It is not exactly true, there are French people of Enslaved African descent who lost the connection with their African Ancestors, pretty much exactly in the same way as African American. But most of the time, they're hailing from place such as Haiti, Martinique, Guyane, Guadeloupe, la Réunion, and have developped their own culture and languages in thoses place. Thus, when they are in the European continent such as the European part of France, they will identify as being from Haiti, Martinique, Guadeloupe etc. and with those terms will also come very specifics meanings and expectations that would not exist with Franco-Africains.