There is also a 2006 BBC TV movie titled Lady Chatterley starring Sean Bean. If that is the version you have, it is originally in English , meaning subtitles might not be necessary unless you are hard of hearing (in which case you would search for "English SDH").
The 2006 French film Lady Chatterley , directed by Pascale Ferran and featuring Marina Hands, offers an Extended European Edition spanning nearly three hours, with English-subtitled, two-disc releases available. You can find this acclaimed, longer version on eBay and Amazon . Lady Chatterley (DVD, 2006) for sale online - eBay lady chatterley 2006 english subtitles exclusive