A pair of blue jeans carries the names of two European cities. Denim names one of them, and jeans names the other.
Denim comes from the French serge de Nîmes, "serge from Nîmes." Serge is a twilled cloth, and Nîmes is a city in southern France. Say "de Nîmes" quickly in English and you arrive at "denim." Etymonline dates the word in English to the 1690s.
The first denim was probably not the cotton we wear. Etymonline says it was originally a kind of serge. Etymonline traces serge through Old French sarge and Medieval Latin sargium to Latin serica, "silken garment." The Guild history of denim notes that "serge" covered woollen, half-woollen and silk twills. Etymonline records the meaning "coarse, colored, twilled cotton cloth" by 1850, in American English.
The city's own name is older still. Etymonline gives it as Roman Nemausus, said to come from a Gaulish word, nemo, "sanctuary."
The second city is Genoa. Wikipedia explains that "jeans" comes from Gênes, the French name for Genoa. A sturdy fabric from 16th-century Genoa was used for workwear there, including by the Genoese navy. In Wikipedia's account, weavers in Nîmes later tried to copy it. They ended up with a similar twill, which became known as denim.
The garment came much later, and in America. In December 1870 the tailor Jacob W. Davis began making work pants reinforced with metal rivets. He bought his cloth from Levi Strauss & Co., a San Francisco dry goods firm. On May 20, 1873, Davis and Strauss received US patent No. 139,121 for an "Improvement in Fastening Pocket-Openings."
The word for the trousers took its time too. Etymonline records "denims," meaning denim pants, from 1868, when they were usually overalls. Wikipedia notes that Levi Strauss kept calling its flagship product "waist overalls" rather than jeans until 1960.
So the name on the label of the most American of garments is French. It remembers a town that was famous for a woollen cloth, not for blue cotton pants.