Hotel/Hostel Late Check-in
Most hostels and hotels don't care what time you check-in, simply because they have staff manning the reception 24h. Nevertheless, it is good policy to warn them in advance if you plan on arriving late, to avoid them considering you as a no-show and cancelling your booking.
In your case, I would say that midnight is not really a late check-in per se. So I would not be worried. To be safe, email the hotel/hostel and ask.
Night Transport in Paris
You can check the departure times of public transport lines (RER, Metro, Bus, etc) on the RATP website here (sorry the page exists in French only, but google translate is your friend). Timetables vary between weekdays (Monday - Thursday), weekend days (Friday - Saturday), and "rest days" (Sunday).
Generally speaking though, public transport in Paris never stops. When the Metro/RER stops working, their journeys are replaced by night buses (Noctiliens), marked with a starting N on the bus number.
Your Arrival in Bercy
From your premises I assumed you were landing in some god-forsaken place like Beauvais. Instead arriving in Bercy means that you are already in Paris. The Bercy Metro station is served by the Metro 14, which takes you towards the centre, and the Metro 6 which takes you all-around the city to its west side. Here are the first and last trains from Bercy on Monday 22/12. So I would say pick any hostel with good reviews and go for it.