Sophie Lionnet, 21, from Troyes in northeast France, was living in their £900,000 home after being hired to look after the couple’s children.
Her father, Patrick, 56, said that he last heard from his daughter in July when she sent him a postcard in which she talked of tensions in the family and coming home soon.
Mr Lionnet, who works for the municipal park service in Troyes, told local newspaper L’Est Eclair: “Nothing indicated that it was so serious. If it had, I would have gone to join her.”
He was told of her suspected death on Friday, although the remains found in the garden have yet to be identified.
He added: “It’s unthinkable. I don’t know if I can stand up to the shock or collapse.”
Ms Lionnet moved to London last year to improve her English. She described herself on Twitter as “seeking a universe of cinema and/or dance, theatre, films”.
Her cousin Mélanie Lionnet said she was “kind and had unlimited patience”.
She added: “She put an enormous effort into her work and that took it out of her.
“She did everything for [the children]. Coming back to France was a relief for her but it was also sort of abandoning the children.”
Friends described her as a “rock” to the two boys in her care, but claimed she had been “unhappy” for some time.
She was reportedly due to fly back home to France last Monday but never arrived.
Police were called to the property last Wednesday following reports from neighbours about a “weird barbecue” in the grounds of the house and a “foul-smelling smoke”.
Police have been unable to tell the age or gender of the dead person because the remains were so charred.
Kouider, 34, a makeup artist and designer, is the former girlfriend of Mark Walton, who was part of the initial lineup of the boyband Boyzone.
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Alleged killers, Sabrina Kouider and her partner Ouissem Medouni