Applications for a Chinese L (tourist) visas in the United States can't be mailed directly to the Chinese Embassy/Consulate. As a result, many people use third-party agencies who accept applications by mail and drop them to the proper Chinese Embassy/Consulate.
I read on the website of one such agency, http://www.mychinavisa.com/special-requirements (mirror):
Citizens of certain countries, such as France, Turkey, Nigeria, etc., are required to apply in person at the Chinese Embassy/Consulates. The list can change without notice.
I didn't see this restriction on the other agencies' websites I have looked at.
Can't French citizens in the United States apply to a Chinese L (tourist) visa through an agency?
I'm interested in the case where the French citizens are also permanent resident of the United States (= have a green card).