For example, 70 is soixante-dix, literally “sixty ten”
80 is quatre-vingts, literally “four twenties”
90 is quatre-vingts-dix, literally “four twenties ten”
I don’t understand how French could have lost names for these numbers since Latin.
First of all, those names are not lost.
While quatre-vingts-dix and the others are the most commons in France and its former colonies, other French speaking countries (e.g. Belgium and Switzerland) still use more regular names:
Septante instead of soixante-dix (70)
Huitante (or more rarely Octante) instead of quatre-vingts (80)
Nonante instead of quatre-vingte-dix (90)
In fact, the French government tried to reintroduce them in France in 1945 without much success.
So, what's about those 20s everywhere?
It's important to note that the roman numerals are not as decimal as they look: they're not using decimal digits, half-decimals (5, 50) are really important too, numbers smaller than 1 are usually dealt in multiples of 1/12 instead of 1/10, ...
This inconsistency comes from the fact that the roman system was generally guided by a simple objective: practicality. Even common rules we use today (like writing IV instead of IIII for 4) was inconsistently applied depending on the circumstances.
This shouldn't come as a surprise that during the middle ages, peoples started to tweak this system to their need.
One innovation was the exponent notation "n^m " which meant "n groups of m". While I present it as a general notation, we only have traces of two usages: "n^C " to mean "n groups of 100" and "n^(XX)" to mean "n groups of 20".
You can still see trace of the former in modern English, where it's common to says "fourteen ninety two" instead of "thousand, four hundred and ninety two".
The latter was particularly popular in France where for exemple "IIII^(XX)" became commonly used for 80.
Going into through the Renaissance, the decimal naming and the vingesimal naming were both widely used within the French population for numbers. But in 1635, the Academie Francaise is created, with for task to codify the French language. In their first dictionary in 1694, they push for the compromise of using decimals numbers except for 70,80,90.
A century later, the French revolution happened. And one of the major objectives of this revolution was to unify France in a single indivisible entity, with a single uniform language. In particulars, no regional alternatives for numbers would be tolerated, both in administrations and in schools.