We have produced for the first time a detailed velocity map of the giant filamentary nebula surrounding NGC 1275, the Perseus clusters brightest galaxy, and revealed a previously unknown rich velocity structure across the entire nebula. We present new observations of the low-velocity component of this nebula with the optical imaging Fourier transform spectrometer SITELLE at CFHT. With its wide field of view ($sim$11$times$11), SITELLE is the only integral field unit spectroscopy instrument able to cover the 80 kpc$times$55 kpc (3.8$times$2.6) large nebula in NGC 1275. Our analysis of these observations shows a smooth radial gradient of the [N II]$lambda$6583/$text{H} alpha$ line ratio, suggesting a change in the ionization mechanism and source across the nebula, while the dispersion profile shows a general decrease with increasing distance from the AGN at up to $sim 10$ kpc. The velocity map shows no visible general trend or rotation, indicating that filaments are not falling uniformly onto the galaxy, nor being pulled out from it. Comparison between the physical properties of the filaments and Hitomi measurements of the X-ray gas dynamics in Perseus are also explored.