When I saw this in its brief American release, I took the word of a Japanese-speaking guy at work, who didn't go to films but had seen the poster, that "kaseki" meant ashes. Heading a film that ends with a teary, agonized exclamation, it made sense; I took his word and never checked. "Ashes" carries a sense poetically similar to "fossil," and might have been subtler: ashes; tears; emotional entropy; fossil emotions. But my old dictionaries offer only "fossil." Ka is kanji for change and seki is stone, so petrified dinosaur. "Kaseki no mori," title of a Shinoda film two years earlier, means petrified forest. "Kaseki", which I've been desperate to re-see for 20 years or so is but didn't feel at all long, in crisp, if I recall, perfect color, fitting to the joy, yet ironic to the pall, cast by the story. The Paris sky may have been always or mostly overcast. (But see my mis-remembrance of the character Anne in "The Aviator's Wife".)
A by no means ancient, sixty-ish, businessman goes with a much younger subordinate to Paris on business. There he suffers an attack, diagnosed as terminal cancer. I can't recall whether before or after the diagnosis, he's attracted to the Japanese wife of a highly placed Frenchman, a striking woman who may be nearly as old as he is. The diagnosis gives him courage to befriend her. No one's likely to see this here, but I won't give away the shattering unguessable conclusion.
Actress Haruko Sugimura plays both the diplomat's wife and Death. Subiela's 1992 "El lado oscuro del corazón "is a touchpoint for "Kaseki "and I mention "Kaseki" in that review.