In that article, I marked a few comments with asterisks so that I could elaborate on them later. None of these embellishments negate what Michael posted; I'm just adding a few details to their lives during prime-time.
She visited Grace Brothers with a dog to buy him some clothes. (Yes it is a different breed, but it would seem that since she loves them so much, she must have more than one.*)
At some point after that trip to Grace Brothers, Mrs. Chase lost both her husband and her poodle Roger. Either they both had died - perhaps together in a car crash on the way to the vet? - or the Chases got a divorce and Mr. Chase got custody of Roger.
So one way or t'other, Mrs. Chase must have consoled herself by getting a new dog and by forgetting her troubles with a trip to Torquay.
Based on the facts of her past history in the series, she seemed to have worked early on at Grace Brothers*, as well as a His and Hers perfume model... as seen in these pictures:
However, at no point during the episode "His and Hers" is her name actually given; and she is never addressed as "Miss French". The name doesn't even appear in the end credits - not that I've ever given any weight to the end credits in the past.
Maybe two of the most horrid people in the comedy world got to share a great moment together*.
Here's the scene in which John Cleese and Eleanor Bron made cameos on 'Doctor Who' as snobby, pretentious art patrons in a Parisian art gallery:
I think MIchael is right - the actors were actually appearing in 'Doctor Who' as Basil Fawlty and Patsy's Mother. (She never was given a name on 'AbFab'.)
They probably only just met in the museum that day, but the experience of seeing the TARDIS vanish gave them a bond shared by very few in the World of the Toob. And because Basil could easily succumb to the base nature of his human frailties, and because Patsy's Mother was prone to be - well, let's face it, a slut - then I think it's pozz'ble, just pozz'ble, that the two of them ended up in a Parisian hotel room together that day.
Paris... "The City Of Little Deaths" if you know what I mean. Nudge nudge wink wink.