SLDInfo has the best answer yet on why France didn't go to NATO for help...

via SLDInfo.

It is most important to note that when President Hollande declared a state of war with ISIS, he deliberately chose to invoke Article 42.7 of the Lisbon Treaty, not Article V of the NATO treaty.
Article 42.7 is the “solidarity clause” that states if a member of the European Union is the victim of “armed aggression on its territory”. other EU member states have an “obligation of aid and assistance by all the means in their power.”
In essence, France chose to work within a European framework, without formally drawing in NATO and the U.S. direction that would entail.

If that isn't juicy enough for you, check out the reality of the Iranian nuclear deal...

When analysts and intelligence experts were highlighting the warming sun of the Arab Spring, there was much hope: democracy was in the air and the gap between Islam and the West might be closing.
Rather than a warming sun, close observers felt an icy chill from the events of this Fall in Paris, and an evident European strategic shift away from the agenda set by Washington.
Major changes in geostrategic forces began when the U.S. President backed off his Syria Red Line, and then pushed relentlessly his own objectives with Iran while dismissing French, Israeli, and Gulf Arab reservations to the U.S.-Iran accord.
The Russian decision to accept Assad’s invitation to intervene militarily in Syria, and enlarge its military base presence there laid down an historic marker for a significant reconfiguration of power, not only in the Gulf, but also the entire Eastern Mediterranean region.

So not only do we have the answer to the oft asked question of why France didn't evoke article 5, but we also have a warning...one I've been making since the start of this mess.

"a significant reconfiguration of power" 

We can already look to the future on this one.  The Obama admin's signature foreign policy achievement will be hailed as nothing but a failure