The autumnal equinox occurs on MJD 55827.378 (2011 Sept. 23 09:04 UTC) or 9h13 in the morning, Paris mean time. Therefore, according to the rule in effect during the French Revolution, MJD 55827 (23 September in the Gregorian calendar) will be the first day of year CCXX in the Republican Calendar.
According to the rule used by Brumaire, including their iPhone and iPad apps, MJD 55827 is also the first day of the 220th Republican year. The day before, MJD 55826 (22 September), is a leap day according to Brumaire, but not according to the official calendar rule. Dates prior to this are different by one day, but with the start of the new year, dates will be the same by both rules until 2014.
The first month of the Republican calendar is Vendémiaire, so New Year's Day is 1 Vendémiaire. Happy new year!