In this paper, second in this series, we discuss the nature of 66 faint carbon (C) stars which have been discovered by scrutinizing the plates of the First Byurakan Survey (FBS). These plates display lowresolution spectra of objects located at high Galactic latitudes and have a limiting magnitude of about V = 16. Our sample of 66 objects is part of a total of 120 stars found in the FBS and confirmed spectroscopically to be C stars. These 66 objects are those which show early-type spectra (not N-type). To better characterize these objects, medium-resolution CCD spectra were obtained and are exploited for them all, together with consideration of their 2MASS near-infrared (NIR) colors and their optical variability. First, we establish criteria for getting a spectral classification by using our medium-resolution spectra. Then, 57 objects show spectral features which are typical of CH-giants, while four can be classified as a R-type stars. Five objects in our sample are reported to be probably carbon dwarfs according to previous studies. We derive effective temperatures from photometry. Finally, the optical variability of our objects are studied by using the data of the Catalina Sky Survey (CSS). It is found that the vast majority do not display variability. However, for some of them, the phased light curve may indicate the presence of a secondary component. We estimate the detection range (in kpc) for each class of carbon stars detected in the FBS. Finally, our studies of C stars found at high galactic latitude are discussed in the context of the Gaia mission.