I am a UK citizen, my wife is a non-EU/EEA/Swiss Citizen who holds a UK Residence Permit. Her mother would like to visit us and travel with us to France over Christmas, my question is which visa should we be applying for? She currently holds a UK short stay visa (1 year multi entry) so travelling to the UK isn't a problem. However she isn't dependent on us financially, though we will be paying for the trip, so it seems like she cant apply for a family visa due to this?
Because your mother in law is independent of you and your wife, you are right that she cannot benefit from the free visa specified in the EU freedom of movement directive. She therefore needs whatever document she would need if she were visiting the Schengen area without you: a Schengen visa (unless she is traveling with the passport of an "Annex II" country) plus, of course, her passport.
The free movement directive extends to a non-EU parent or other relative in the ascending line (including the ascending line of the spouse or partner) only if the relative is a dependant, a member of the household, or in need of "personal care" (Article 2(2)(d), Article 3(2)(a)). Your mother in law appears not to qualify.