InfraRed (IR) astronomical databases, namely, IRAS, 2MASS, WISE, and Spitzer, are used to analyze photometric data of 126 carbon (C) stars whose spectra are visible in the First Byurakan Survey (FBS) low-resolution(lr) spectral plates. Among these, six new objects, recently confirmed on the digitized FBS plates, are included. For three of them, moderate-resolution CCD optical spectra are also presented. In this work several IR color-color diagrams are studied. Early and late-type C stars are separated in the JHK Near-InfraRed (NIR) color-color plots, as well as in the WISE W3-W4 versus W1-W2 diagram. Late N-type Asymptotic Giant Branch (AGB) stars are redder in W1-W2, while early-types (CH and R giants) are redder in W3-W4 as expected. Objects with W2-W3 > 1.0 mag. show double-peaked spectral energy distribution (SED), indicating the existence of the circumstellar envelopes around them. Twnty-six N-type stars have IRAS Point Source Catalog (PSC) associations. For FBS 1812+455, IRAS Low-Resolution Spectra (LRS) in the wavelength range 7.7 ÷ 22.6 μm and Spitzer Space Telescope Spectra in the range 5 ÷ 38μm are presented, clearly showing absorption features of C2H2 (acetylene) molecule at 7.5 and 13.7 μm, and the SiC (silicone carbide) emission at 11.3 μm. The mass-loss rates for eight Mira-type variables are derived from the K- color and from the pulsation periods. The reddest object among the targets is N-type C star FBS 2213+421, which belongs to the group of the cold post-AGB R Coronae Borealis (R CrB) variables.