The days of the Revolutionary Calendar's ten-day week were named first, second, third, etc, but what about the months? The most logical thing would have been to call them first, second, etc, too, and this system was suggested, though it never caught on.
So what can you call your months? There was an enthusiasm for basing French society on Classical Roman lines, but unfortunately the months of the French year were already based on classical Roman lines, and the revolutionaries wanted a complete change.
Well, how about calling the new months after...er...
Hmm...well, yes, the South of France, it has a climate superb, and a system such as that would proclaim to the world...
...oh. On the Parisian weather.
Oh well. If one must.
Vendémiaire (grape harvest) Brumaire (mist) Frimaire (frost) Nivôse (snow) Pluviôse (rain) Ventôse (wind) Germinal (germination) Floréal (flower) Prairial (meadow) Messidor (harvest) Thermidor/Fervidor (heat) Fructidor (fruit).
(The year started, in case you're wondering, at the Parisian Autumn equinox.)
Unfortunately this system faced the population with five months of mist, frost, snow, rain and wind, and so you can see why the calendar didn't survive the arrival of Napoleon, who came from a much warmer place.
They went back to the Roman system of rather random gods.
Nuts and Bolts: thing to consider today: what would you call the months of the year?
Please don't forget Australia, Russia, and the Solomon Islands in your deliberations.