A young child in France during the First Republic (in particular, one born on a date between 1793 and 1804) might be a plausible candidate. One of the many reforms attempted in this period was to remake the calendar on what they deemed more “rational“ lines - twelve months named for natural phenomena, each month split into three decades, each decade containing ten days. The five or six additional days that didn’t fit neatly into a decade were deemed sansculottides, and supposed to be treated as holidays.

For example, the coronation of Napoleon took place on 11 Frimaire, year XIII of the Republic. Or, to give a date you would recognise, 2 December 1804.

An adult whose memory extended earlier than 1793 would have been taught the traditional seven day Gregorian calendar, and would remember its norms…but a child in that span might well have learned both, or the new system alone, and if asked the date could give it differently than you would.