Paris Flea Markets open during the week?

The biggest flea markets at St Ouen are partly open on Mondays as well. Not every stall will be open... but you'd need several days to browse them all anyway.
Don't expect great deals though, it is quite expensive / upscale (and it is not easy to identify what is bargainable and what is not). And Porte de Clignancourt (the nearest metro stop) is not the safest area, so watch your belongings as you make your way to the market and back. Nothing to be afraid of, just have to be more attentive than usual.

Alternatively, there are plenty of antiques shops in the "Village Suisse" just south of Champ de Mars. The location is odd - at the ground floor and in the basement of a 1970s housing complex - and many shops have been sitting empty for years now, but there are still quite a few! Definitely the largest concentration of antiques stores outside St Ouen.

Here at 2 links:

The Culture Trip: https://theculturetrip.com/europe/france/paris/articles/the-9-best-vintage-clothing-stores-in-paris/

A Top 15 Listing: https://www.france-hotel-guide.com/en/blog/vintage-clothes-shops-paris/

Hope this helps.