The PBS subchannel MHz has some French-made series in its “International Mystery” line-up:
http://www.mhznetworks.org/programs/mystery-drama
Tonight, Monday, July 8th, they are starting a re-run of Season One of “Spiral”:
(two episodes each Monday for four weeks, the entire eight-episode first season – this showing is a set-up for Season Two (of four so far; two more in the pipeline), starting next month)
“Spiral” is very edgy, gritty, high-end cinematic stuff, and can be difficult to follow. But it’s a monster hit in France and internationally.
The French law enforcement and legal systems are very different from Anglo-American ones, so it can be hard for American viewers to tell who’s doing what, and whether they should be or not. Even native French speakers have trouble keeping up with the rapid-paced urban patois that the characters use.
If you’d settle for some lower-brainpower stuff, there’s “Inspector Maigret” on Tuesdays, and “Frank Riva” (Alain Delon!) on Thursdays (ending its run soon; re-starting on Saturdays in a few weeks). “Blood of the Vine” has concluded its run, but may show up again. “Maigret” might be the best starting place for someone wanting to work on his/her French.
This is more French programming than MHz usually runs; their staples are Italian and Swedish series. Everything is sub-titled (except an Australian series, which needs it – regional accents, immigrant Asian characters; even the Australians have trouble with it).
Station listing:
http://www.mhznetworks.org/mhz-worldview/carriage
On-line:
http://www.mhznetworks.org/mhz-worldview/live
Various platforms: