French marigolds (Tagetes) or Calendulas? French marigolds are not hardy, so they'll die. Calendulas ('Pot Marigolds') often survive the winter, or seed themselves.

Unfortunately marigolds hail from sunnier climes and are annuals so won't survive the British winter.

I grow English marigolds and when they have died off I just put the pot in the greenhouse(unheated) for the winter and in the spring/early summer they come through ... took me ages to get real English marigolds - at one garden centre the young assistant said she had never heard of them !!!!!!!!!!
I also get lots of seeds from them so the original packet I bought has been well worth it .... Val