My impression is that "serie" is not exactly "obsolete" so much as it is more stigmatized now than it was in the past (maybe a similar example would be the use of "I" in contexts like "between you and I"). Although I associate singular "serie" with non-native speakers, I believe it is also used by some native English speakers in the present.
It's not clear to me that serie was ever the usual form of this word in English. The Oxford English Dictionary has examples of singular series from as early as 1618. The OED entry for serie says "Often criticized in usage guides from the mid 20th cent. (and earlier in N.E.D.: see quot. 1884) as incorrect or nonstandard, and still not common."
As you mentioned, series is used as a singular in English because that is the singular form of the word in Latin. There are many words where English uses a fully Latin spelling but French or another Romance language uses an adaptation: e.g. English thesis vs. French thèse or Italian tesi.