Yes, your finding of "collège" is apt - and your excuse about different languages using homonyms for different meanings is not - at least not in this case. Because, if you had continued your research, you would have found that the English word is a descendent of the French word around the 14th century which comes directly from the Latin "collegium."
Being descended from latin is irrelevant.
Right now those are different words in different languages with different definitions.
The original argument (which I am arguing against) is that the game,
in its english version, uses the word "college". And that this word can also mean middle school.
However, this word is used in an english sentence. Meaning it is using the english word and thus the english definition.
Not the latin word, not the french word, not the german word, nor any other latin based language.
In fact, borrowing words and then altering them is the most common reason for having homonyms in different languages with different definitions.
Because those are different languages
I was trying to investigate if there really exists an ENGLISH dialect where people use the ENGLISH word college in an ENGLISH sentence to indicate a middle school.
So far all I found is that in french they use a very similar (but not exactly the same, there is an epee symbol) to indicate a middle school. but you wouldn't expect such a random placement of french word within an english sentence in an english game. and as such there is no ambiguity about what this game means by the term college. (it means place where adults go to learn after graduating from K12 education)