The previous answers are correct that this is a case for the British 6 Pounder Naval gun, which was adapted from a French hotchkiss design. From the stampings, this case is a mark 3 case made at The Royal Laboratories, Woolwich, London in 1904. It was loaded on 20th February 1904.
The arrow above the "N" is a naval acceptance stamp. The "C.FF" indicates that it has been fired twice with a full charge of cordite propellant. The A in circle with the dot next to it indicates that the case has been annealed (heat-treated to soften the brass) once.
The I in the circle indicates that the case was fitted with an improved primer, which was then replaced with the screw-in type which is fitted. The star after the III presumable indicates that the case was modified to take a screw-in primer.
The primer that is in the case is a mark 3 type screw-in primer, which was made at the Royal Laboratories in Feb 1911. Your case appears to have been fired twice previously between 1904 and 1911, then reloaded and fired once again.
It never got an "F" stamp to indicate that it had been fired once again as it found it's way home with a sailor after the 3rd firing, and then found it's way to you today.
Sorry I don't have a photo of a complete one, but it would likely have been fitted with a pointed steel HE projectile with a fuze in the base.