Can I use a first class Japan Rail pass to board trains that don't have a first class carriage?
Most JR trains have Ordinary Cars (coach class) while many long-distance trains also offer Green Cars (superior class). With a Green-type JAPAN RAIL PASS you can use either class.
Note that there's only a Green Japan Rail Pass, not a "first class" one. This means you can use Green Cars (roughly, business class), but you cannot use the recently launched Gran Class (roughly, first class) cars without paying additional surcharges.