The Meet the Parents actress explained that the family are already fluent in Spanish and are now working on a new language.
"My daughter's doing a film in Spain now, because she's fluent in Spanish. I'm delighted," she told The Sun.
"The children are fluent in Spanish too, so the whole family is now learning French. Gwyneth is the quickest learner I've ever met in my life."
Danner added that she is fond of her son-in-law Chris Martin's music with Coldplay, as he has written songs for big moments of his family's life.
She said: "One of the most famous ones - which I weep to every time I hear it - is 'Fix You'. He wrote that for Gwyneth when her father Bruce died - he missed meeting Bruce by a couple of weeks."
Danner recently joined the cast of ABC pilot Gilded Lilys, from Grey's Anatomy creator Shonda Rhimes.
Paltrow will next appear as Pepper Potts in The Avengers, which opens in the UK on April 26 and the US on May 4.
Watch the video for Coldplay's 'Fix You' below: