How much of Downton Abbey (TV) should you watch to prepare for the movie?

While I have yet to see the film, I have read about the film's plots.

And while I also think someone probably can jump into the Downton Abbey film and enjoy it as long as they have some knowledge about whom the characters are and/or the dynamics between them, I think one would still benefit from watching the entire TV series first, as the events of the final season of the TV series do dramatically change the situations of some the characters whether we are talking marriage, job-changes, or social status, while other characters don't change or advance greatly.

In example one on-going plot of the TV series revolves around the job status and sexual orientation of the Footman Thomas Barrow, who's also a very vein and manipulative character full of self hate that he often takes out on many of the other servant characters.

By the end of season six Thomas has become

Downton's head butler, as Mr. Carson has a medical condition that keeps him from remaining the head butler. In addition Thomas has a had a lot of mishaps in looking for love and ends the series rather unrequited, even attempting dangerous medical experiments to change himself and shortly thereafter, attempts suicide!

And so one of the plots of the 'Downton' Film is

Thomas finding someone who loves him in return, despite that they may never meet again, while the film also world builds with exploring homosexuality in this era a bit more. In addition the film's former dynamics come back into play with Mr. Carson returning as head Butler for a particular event happening at the Abbey.

One might not appreciate this romance and exploration, if one didn't know all the trials Thomas went through to even get here.

Does it help at all to have watched any of the TV series? (Surely, yes?)

Obviously, yes.

If so, how much do you need to have seen to get the most value out of the movie? Are the later seasons that important to following the movie?

The movie takes place after the last season of the show, so, if anything, the later seasons are the most important. That being said, the movie starts with a recap of the entire show (and it is spoiler-filled, in regards to all seasons of the show) which gets you up to speed before the new plot begins.