Flat and wide-bandwidth gain spectrum, along with phase-sensitive gain with no need to generate amplifier input idlers, can be achieved with a coupled dual-core fiber optical parametric amplifier. In this paper, we analyze the noise properties of such an amplifier. We achieve a 3 dB noise figure in the phase-insensitive case and a minimum of -6 dB noise figure in the phase-sensitive configuration. An alternative phase-sensitive configuration is also studied, that avoids the use of idlers at the input of the amplifier, leading to a 3 dB flat spectrum combined noise figure for the output signals. Pump transfer noise in phase-insensitive and phase-sensitive configurations is also studied along with the noise figure variation against the length of the amplifier.