I live and work in the USA. While here, I transitioned to a different visa while in the USA and as such, I do not have a stamp for my new passport. I intend to visit my family and secure this stamp in December. However, I'm aware there's a looming threat of a shutdown. In the event of such a shutdown, would the Paris embassy still handle H1-B appointments and process passports?
There are many summaries online of which parts of the government continue to function in the event of a USA government shutdown. Here is one from Reuters:
U.S. embassies and consulates would remain open. Passport and visa processing would continue as long as there were sufficient fees to cover operations. Nonessential official travel, speeches and other events would be curtailed.
So a given embassy is likely to continue processing visas, at least for a while.