During the reign of Philip II Augustus (1180-1223) and, more specifically, after 1190. In this year, Phillip first used the title Rex Franciae (King of France) on his royal seal, in contrast to the tradition style Rex Francorum (King of the Franks). Rex Franciae is used more and more in documents for the next decade and a half until, in 1204, Philip changes his official style, with which he opens all of his acts, to Philippus Rex Franciae. The term Regnum Franciae (Kingdom of France) appears first in 1205, once again in contrast to the older Regnum Francorum (Kingdom of the Franks).

This is when historians have traditionally located the change from West Francia to France, although there may be earlier instances of Regnum Franciae that I don't know of. The impetus for the change appears to be the growing rivalry between Philip and King Richard I Lionheart of England, who used the style Rex Angliae (King of England) - once again to be contrasted with the older Rex Angolorum (King of the English). It's interesting, and perhaps entirely coincidental, but 1204, the year that Philip decisively plumps for Rex Franciae, is also the year that he conquered Normandy, the most important Plantagenet possession in France and put King John of England firmly in his place (from a French viewpoint!)

This is a very teleological question and has no real answer. It is however generally accepted by historians to refer to France as "France", from 987 onwards. On that date Hugo Capet was crowned King of the Franks, succeeding the last Carolingian king and founding the Capetian dynasty, which would rule "France" for centuries to come.

Is this just repeating what I posted? Ah well, good that it got attention anyway.