Thomas Carlyle, The French Revolution, a History, Chapter 3.4.IV:
...on the 5th of October 1793, after trouble enough, they bring forth
this New Republican Calendar of theirs, in a complete state; and by
Law, get it put in action...
For the Romme (Revolutionary) Calendar, in so many Newspapers,Memoirs, Public
Acts,has stamped itself deep into that section of Time: a New Era that
lasts some Twelve years and odd is not to be despised.
The New Calendar ceased on the 1st of January 1806. See Choix des
Rapports, xiii. 83-99; xix. 199.
Thus with new Feast of Pikes, and New Era or New Calendar, did France
accept her New Constitution: the most Democratic Constitution ever
committed to paper.
As is evident from Carlyle, the calendar was in widespread use during the period of Jacobin (the far left political wing of the the revolutionary movement that became dominant in French politics in 1792-3) domination, for two reasons, in spite of the inertia factor that you mentioned: Patriotic zeal amongst those who were indeed patriotic, i.e. supported the Jacobins; fear of being deemed "Suspect", i.e. opposed to the Jacobins, amongst those who were not quite so 'patriotic': Moving to a new calendar was more palatable than moving the location of your head from your neck to the sack behind the Guillotine...
Carlyle asserts that the Romme Calendar remained in use for some 12 years, through the early Napoleonic era, although radical Jacobin rule effectively ended in the Summer/Fall of 1794, subsequent to Robespierre's execution, less than a year after the calendar was adopted. This was again due to the inertia factor (once the new calendar was implemented, it was difficult to roll back) and because although the radical Jacobins were out of power, the Thermidorians (a somewhat more moderate group who deposed and executed Robespierre in July of 1794, so named because July became the month of Thermidor [hot-sweltering] in the new calendar) also embraced the Revolutionary vision and believed in the "New Era" ushered in by the Revolution, but rejected the unbridled terror and rapidly developing despotism of radical Jacobinism, led by Robespierre.
In the same way, the French accepted other radical innovations of the Jacobins, as cited above from Carlyle.