Cameron and Hollande were more interested in intervening in Syria than the Obama administration was.
Would it have been possible for the two European powers to implement a no-fly zone without the United States at the time, or would it have been an impossibility?
Yes it would have been
easily doable.
Syria sits right next door to Cyprus - the UK's most important oversea's base, and one of its largest. RAF Akrotiri has the capability and facilities to, in relatively short-order, accommodate massive amounts of air power & logistical capabilities - including air to air refuelling (Which the UK & France are pretty decent in - and could potentially have got other logistical support from other EU/NATO nations)
Its from Cyprus the UK smashed Egypt up in 1956 - and its Cyprus which formed a core-component of the UK & USA's own efforts in invading Iraq 2003.
If the will was there, the UK & France had the planes, facilities & logistics to impose a no-fly zone over Syria.
This isn't even considering the Charles De Gaulle, or other RN/French Naval assets which could have also been used imposing a no-fly zone/taking out key targets (I.e. cruise-missiles from SSN's).
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HOWEVER: You forget - it wasn't the USA which bailed on using military force against Syria:
It was the UK - specifically Parliament telling Cameron "NO!" when he wanted authorisation to start bombing Syria - without UK support, the USA
then decided to not use military-force.
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Russia does complicate matters slightly - but they are
vastly overrated. They have global projection capabilities potentially even weaker than Italy's or Spains - while having a economy smaller than Italys.
Against anything the UK or France could
individually put into the Mediterranean - let alone together - any Russian force would have been hilariously outmatched and thus absolutely pitiful in order to try and intimidate the UK/France into backing off - and economically, Russia is less than 84% the size of the UK's own economy (& even less than that for France) - and this is with Russia having a population of 143.5million compared to the UK's 63.23million & France's 65.447million - so a vastly poorer population & nation per person.
Basically, then: sanctions/economic-warfare wise would have been a loosing proposition for Russia (& this is before we factor in EU retaliation). Militarily would be even worse (Since if France/UK ignore Russia and call Russia's bluff... it gets exposed for the powerless hoax it really is, or otherwise gets the Russian Navy massacred by the RN/French Navy & gets into a hilariously one-sided war with NATO in the process I.e. actual military force =
never going to happen).