In the Third Republic (France's political regime from 1870 to 1940), the power was not at the Elysée Palace, but at the Palais-Bourbon, seat of the Chamber of Deputies. Had the rioters succeeded in invading the Palais Bourbon, they would have found most of the ministers there. Of course, it's conceivable that some key figures would have been evacuated (even without helicopters). It certainly would have been the case for the President of the Council (that's how the prime minister was called then), Edouard Daladier.
In OTL, Daladier resisted the calls for him to resign on February 6 and issued clear orders for the Palais Bourbon to be protected and the rioters contained. He only resigned on February 9, when the crisis was over.
Had he been evacuated and the Palais Bourbon taken, he could paradoxally have been freer in his decisions to save the situation. He would probably have gone to the Elysee Palace and ask the President of the Republic to issue orders to the Army to intervene.
Now the President of the Republic, Albert Lebrun, was pretty weak (I cannot resist quoting Charles de Gaulle. About Lebrun, he wrote: "as chief of state, he only lacked two things: that there was a state, that he was a chief"). He might have done what Daladier asked, then again he could have dragged his feet.
There is also the question of the unity of the rioters. The extreme-right at the time was not a united front. What happened on February 6 was not a planned coup d'état. I doubt very much that colonel De La Rocque, the leader of the Croix de Feu, would have gone so far as taking deputies and ministers hostage. He would have been willing to negociate the peaceful evacuation of the Palais Bourbon and then things could have gone back to what happened in OTL, with Daladier resigning and a national unity government being constituted.
Finally, what would have been the attitude of the Army during the crisis? There was a strong anti-republican feeling among the superior officers but still it was the army of the Republic. I don't see the Army siding with the rioters.