There is no train going to or on Mount Fuji itself.
What is your purpose?
(March is outside the official climbing season for Mount Fuji.)
To have a close view of Mount Fuji,
you can visit Kawaguchiko around the mountain,
which is one of the Fuji Five Lakes,
by railway or bus from Shinjuku.
I will have a7-day JR Pass. A 7-day Japan Rail Pass
is too expensive, not suitable just for this round trip.
If you combine Kawaguchiko and Hakone,
a Fuji Hakone Pass may be a good deal.
Here in this forum,
many posters have said Fuji to refer actually to a place around the mountain.
starting from and returning to Shinjuku station Where around Shinjuku Station will you stay?
There exist Shinjuku Stations of five railway operators on many lines;
different Shinjuku Stations have gates of the same or similar names.
You had better know in advance
what gate or entrance for which line you should get to.
- Japan Guide: How to travel between the Fuji Five Lakes and Tokyo
https://www.japan-guide.com/e/e6905.html- Japan Guide: Fuji Hakone Pass
https://www.japan-guide.com/e/e2358_014.html- Expressway bus reservation:
Shinjuku Expressway Bus Terminal -- Kawaguchiko Sta.
https://www.highwaybus.com/gp/inbound/inbPlanList?lineId=110- Busta Shinjuku (Expressway Bus Terminal)
http://shinjuku-busterminal.co.jp/en/
