'Kaki'

is a recently adopted name for the fruit of the tree known botanically as Diospyros kaki.  It has been known for centuries in English as Persimmon, and (again more recently) as Date-plum and Chinese fig...

Persimmons hanging over a wall in St.Antonin-Noble-Val

...and in French as Plaquemine (also a French place-name in Louisiana),  but it is now sold as Kaki in France. 

'Kaki' in French also means the colour khaki, which, perversely is a shade of green, whereas in English it is dust-colored,  and derived from  Urdu  "dusty," borrowed from Persian khak "dust."  

Persimmons were a favourite fruit in the Islamic and Turkish empires, and hang off the trees at this time of year in the gardens of the Alhambra in Granada, as well as - occasionally, here in southern France.

They were originally grown in China several thousand years ago, where they served as a symbol of balance, harmony and equilibrium.  In Japanese they are known as kaki.  Diospyros means 'celestial edible'.

Persimmons are now also known as Sharon Fruit because of their recent mass-cultivation in Israel for export.

They are sweet and somewhat bland, though bitter when under-ripe.