French capital vs City of Light

French capital and City of Light both are nouns.

Word	Noun	Adjective	Verb	Adverb
French capital	Yes	No	No	No
City of Light	Yes	No	No	No

As nouns, French capital and City of Light are synonyms defined as:

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

Other synonyms of French capital include capital of France, Paris.

French capital (noun)	City of Light (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