Hi Ravil,
I'm sorry to report, but Vaux-le-Vicomte is mostly closed from Nov 9 till March 15,
except for their Fête de Noël from Dec. 20 till 4 Jan. (although they're closed on Dec. 25 and Jan. 1 during that period). See the
Vaux-le-Vicomte schedules page (in French). Although, if you happen to be there for that special Christmas period, I would imagine it's quite the sight, with the chateau & gardens lit with Christmas decorations. I visited the chateau two weekends ago during the day and the garden is quite impressive.
The chateau is privately owned and thus I guess they can keep whatever hours they please.
There is a
shuttle bus between Melun and Vaux-le-Vicomte, but it doesn't cover the Christmas period and stops at the end of October. Otherwise, taxi is the only other option. Distance between Melun and Vaux-le-Vicomte is 6km so maybe about 15-20€ for the ride.
Best regards,
Ben