ancien regime vs regime

ancien regime and regime both are nouns.

Word	Noun	Adjective	Verb	Adverb
ancien regime	Yes	No	No	No
regime	Yes	No	No	No

As nouns, regime is a hypernym of ancien regime; that is, regime is a word with a broader meaning than ancien regime:

ancien regime: a political and social system that no longer governs (especially the system that existed in France before the French Revolution)
regime: the organization that is the governing authority of a political unit

Other hypernyms of ancien regime include authorities, government.

ancien regime (noun)	regime (noun)
a political and social system that no longer governs (especially the system that existed in France before the French Revolution)	(medicine) a systematic plan for therapy (often including diet)
	the organization that is the governing authority of a political unit