"possible", "impossible", and their negations (like many other adjectives) can take a "FOR ... TO ..." clause as subject .
Leave out "on the basic level"; it just specifies what kind of understanding (basic) is meant.
The structure is
"
FOR a Russian or French person TO understand his music is not impossible."
where the italicized portion is the subject.
A few inversions take place before the final form is reached, but I think you can see that the FOR-phrase is the subject of a dependent infinitive clause, the TO-phrase is the predicate of the same clause, and all together the non-finite clause (FOR ... TO ...) is the subject of the main clause.
Alternately, the FOR-phrase simply acts as a variant of an IF-clause:
"... not impossible to ... basic level, IF ONE IS a Russian or French person."
If we took a poll, I wouldn't be surprised if the alternative were the more likely interpretation.