Curiously enough, the second part of "flacon" does have something like this meaning in French, although it is more usual to use it as a term of abuse, something like "a**hole" or "s**thead" in English. It can also be used as an adjective to mean "stupid" or "idiotic." The French like this word and its variant "connard," which is generally used to mean something like "fool" or "idiot." A more polite word for the female part is "chatte," which has the more endearing feel of "pussy" in English, kind of warm and furry.
The French word for whale, however, is "baleine," so I don't see where the whale comes into it... (Ahem [cough cough]). "Blanc de baleine " is spermaceti. (Don't get nervous, boys, this is just the stuff they used to burn in those whale-oil lamps they used in great-grandpappy's day.)
BTW, a lot of the French-speaking SAs I've encountered in the States don't use the word "flacon" at all when referring to the container; they say "bouteille" (bottle), perhaps under the influence of English. Hélas... ce qu'ils font de notre belle langue!