Does French past participle PRISE explain Modern English meanings of "comPRISE"?

Your etymology is not exact; "comprise" does come from French, but the French word at the origin is "compris(e)", past participle of "comprendre". As to the French word "explaining" the English, you can't indulge in such characterizations without quoting them and making clear what you intend to convey thereby. The meaning of the word "comprendre" can only provide certain clues; for instance the meaning "to grasp with the mind" is obsolete and insofar as that goes, "comprendre is certainly no "explanation". However, in the sense "include, contain", it is true that one of the meanings of "comprendre" is quite similar in French.

(Etymology from the SOED)

Comprise indeed didn't pick comprendre but the past participle compris as its basis.

Comprendre means according to its Latin etymology comprehendere "to take together".

Old French had both comprehender and comprendre verbs with various meanings including "to grasp, to understand" which gave one of the modern meanings of the French comprendre, but also to seize/invade (lost in modern French) and to contain/include which is alive in both French and the English "comprise".

Comprise isn't a unique case of past participle derivation. Here are a few examples:

Still from -prendre verbs:

• to reprise, French past part. repris vs reprendre (take back)
• to surprise, French p.p. surpris vs surprendre (same meaning)

From -faire verbs:

• to defeat, from old French desfait (now défait) instead of défaire.
• to forfeit, French forfait instead of forfaire.
• to counterfeit, French contrefait vs contrefaire.

Other stems:

• to remise, French p.p. remis instead of the infinitive remettre (send back).
• to corrupt, from the Latin past. part. corruptus instead of infinitive corrumpere (French corrompre)