Two-headed cock was choosed as city symbol of famous Versaille (France). Why?

The two-headed cock is a symbol of the freedom offered by the French
Republic.

"The municipal flag of Versailles is divided horizontally white over
blue in a ratio of about 1:3, it is defaced with the arms of the town,
namely a shield with three three gold fleurs de lis on a blue field in
the base and a double-headed cock in natural colours on a white field
in the chief. The shield is crowned with a mural crown composed of
alternating towers and fleurs de lis...

The coat of arms of Versailles was adopted in September 1789. The
double-headed roaster issuant symbolizes the burgeoning freedom.
Fleurs-de-lys were logically added in chief since Louis XVI was still
King of France when the arms were created. The coat of arms was
painted on the flag used by the National Guards in Versailles."

CRW Flags: Versailles (Municipality, Yvelines, France)
http://www.crwflags.com/fotw/flags/fr-78-ve.html 

"The Support Base of Versailles-Satory (Base de Support de
Versailles-Satory - BSVS) recently recieved its pennant (fanion. The
pennant shows the facade of the Hall of Mirrors (Galerie des Glaces),
in the palace of Versailles, a fleur-de-lys, the double-head roaster
symbolizing the Republic (probably the double-headed roaster issuant
shown on the municipal flag of Versailles, which was designed shortly
before the proclamation of the French Republic)."

Atlas Géographique Mondial: Pennant of the Support Base,
Versailles-Satory
http://atlasgeo.span.ch/fotw/flags/fr%5Eunitp.html

The two-headed cock is a fusion of two famous symbols: a two-headed
eagle was an ancient embem of the Holy Roman Empire, and was widely
used in France and in other European nations. The rooster was a symbol
of the French revolution, and later of France herself:

"One of the national emblems of France, the Coq Gaulois (the Gallic
Rooster) decorated French flags during the Revolution. It is the
symbol of the French people because of the play on words of the Latin
gallus meaning Gaul and gallus meaning coq, or rooster... The rooster
played an important role as the revolutionary symbol, but it would
become an official emblem under the July Monarchy and the Second
Republic when it was seen on the pole of regiments' flags. In 1830,
the "Gallic Rooster" replaced the fleur-de-lis as the national emblem,
and it was again discarded by Napoleon III. Since 1848, the rooster
has been seen on the seal of the Republic (Liberty is seated on a
rudder decorated by a rooster); it was used from 1899 as a motif on
gold 20 franc coins and it occasionally appears on stamps."

Embassy of France in the United States 
http://www.info-france-usa.org/atoz/rooster.asp

More on the rooster as a symbol of France:

Premier Ministre
http://www.archives.premier-ministre.gouv.fr/juppe_version1/ENG/HIST/COQ.HTM

Search terms used:

"two-headed" + "versailles"
"double-headed" + "versailles"
"coq à deux têtes" 

Many thanks are due to my friend and colleague scriptor-ga for his
assistance in this matter.

I hope this information is useful. If anything is unclear, or if a
link does not function, please request clarification; I'll be glad to
offer further assistance before you rate my answer.

Best regards,
pinkfreud

Very usefull, complete and amazingly quick answer! I'm impressed. Thanks a lot!