History and culture are a huuuge part in this. France is a very centralized country, meaning there's Paris (the capital) and the rest of the country. For decades, we have had decentralizing policies so regions and departments could hold more weight but the truth is it's still heavily centralized towards Paris and the "presidential" government. Obviously, we are not a monarchy but that is the feeling you'll get if you're French or living here.
The INF and the academies are in the same vain. But that's not only for football, we have regional/club academies for tennis, rugby, track and field etc. And the all the best young players are detected from those academies and go to the national academy (usually in Paris suburbs obviously). For example, we have the INSEP where our best tennismen (Tsonga, Monfils, Gasquet...), basketball players (Parker, Turiaf, Fournier), athletes (Perec, Diagana, Arron) were trained before turning pro. I believe that when they turn pro, they get to redistribute some of their gains to the country in their first pro years but I'm not sure.
That is administratively speaking. Now France's colonialism past also plays a huge role. The post WWI migrations (Polish, Italian, Spanish mostly), post WWI migrations (North Africans mostly), 70s (Carribeans, West-Africans, Portuguese) make France a huge melting pot in its biggest cities. There are no specific waves since the 80s but the migration fluxes mostly come from Africa. On average, France is less multicultural than the US (there a thousands of villages or small towns which see little to no diversity) but if you simply look at its top 20 cities, it's very diverse.
If you take a look at the history of the French NT, you'll basically see that after one or two generations, the NT starts to be filled with the children of the migration wave :
In the 50s (the first great French generation), you had several players of Spanish (Fontaine), Polish (Kopa) and Italian (Piantoni) descent.
In the 80s (the second one), Italians (Platini is the best example) or Spanish (Fernandez and Amoros are the most known of that era) descent and that's when you started seeng the first great black players (Tigana, Trésor)
The late 90s/mid 2000s (is the third one) where the the Black Blanc Beur thing came. Players from several descents : Arab (Zidane, Lamouchi), Armenian (Djorkaeff, Boghossian), Spanish (Lizarazu, Pires) Carribeans (Thuram, Karembeu), African (Dessailly, Diomède) etc.
So now we are at the 4th generation and we have far more players from African descent reflecting the migration flux since 30-40 years ago.
It is important to say that the players are not immigrants. They are French by law, simply they are of foreign descent like many that allow them to carry several cultures with them. So if you want to replicate the French model, you'll have to follow the same dynamics and also be able to have some centralization in this.