Year of this world coinsist 12 months. Each of months consists exactly 30 days. So one year is 360 days.
Names as follows,

• Spring
  
  • Germinal
    
  • Floréal
    
  • Prairial
• Summer
  
  • Messidor
    
  • Thermidor
    
  • Fructidor
• Autumn
  
  • Vendémiaire
    
  • Brumaire
    
  • Frimaire
• Winter
  
  • Nivôse
    
  • Pluviôse
    
  • Ventôse

Although Icon shows their season(spring as leaf, summer as sun, maple as autumn and snow as winter), there's a simple way to remenber.
Months' name of spring end "-al", summer end "-dor", autumn end "-aire" and winter end "-ôse".

You may notice that from these spell, original of this calendar is came from French.
Named as "Calendrier révolutionnaire français(French revolution calender)", this borned in 1793 as a result of French revolution.

French revolution govnment set Vendémiaire as the first month, and 1st Vendémiaire means our September 22nd(the day when Declaration of Republic was took in 1792).
Each month name was thought out by Fabre d'Églantine, and has a mean.

• Vendémiaire : Month of Grape
  
• Brumaire : Month of Mist
  
• Frimaire : Month of Frost
  
• Nivôse : Month of Snow
  
• Pluviôse : Month of Rain
  
• Ventôse : Month of Wind
  
• Germinal : Month of Seeding
  
• Floréal : Month of Flower
  
• Prairial : Month of Pasture
  
• Messidor : Month of Harvest
  
• Thermidor : Month of Themotic
  
• Fructidor : Month of Fruit

Different to this game, there're 5 days and leap day(belong to no month) after Fructidor.

Although their beautiful month name, this calendar was thrown after only 12 years.
It's because their govenment, seems got compulsion to the decimal, also changed other time units in same time as follows,

1 week(décade) = 10 days
1 day = 10 hours
1 hour = 100 minites
1 minite = 100 seconds

...and simply people got upset.