Ms Noonan, from Co Clare, was living and working in Annonay as an English language teacher.
Police in Lyon and Annonay are both involved in a search operation to find her.
She is not believed to have a wallet, purse or ID on her.
D'Angelo Russell to miss several games with left knee contusion
Russell suffered the injury in a loss in Utah on Saturday night and traveled back to NY with the team to undergo an MRI on Sunday. Russell has been very impressive so far in the early season since being traded from Los Angeles to Brooklyn.
Eimear hasn't been since Wednesday, and had not informed work she would be absent.
She was described as a "warm, bubbly person who had already made a wide circle of friends there through her love of music and singing".
"She graduated last month from UCC with an honours degree in Irish and French, was a talented violinist and to our vast pride was head of the UCC orchestra for her final year there".
"My younger sister Eimear has gone missing in Annonay, France, half an hour outside Lyon", one family member wrote on Facebook.