Paris vs French capital

Paris and French capital both are nouns.

Word	Noun	Adjective	Verb	Adverb
Paris	Yes	No	No	No
French capital	Yes	No	No	No

As nouns, Paris and French capital are synonyms defined as:

Paris and French capital: the capital and largest city of France; and international center of culture and commerce

Other synonyms of Paris include capital of France, City of Light.

Paris (noun)	French capital (noun)
the capital and largest city of France; and international center of culture and commerce	the capital and largest city of France; and international center of culture and commerce
a town in northeastern Texas
(Greek mythology) the prince of Troy who abducted Helen from her husband Menelaus and provoked the Trojan War
sometimes placed in subfamily Trilliaceae