Even back in the analog TV era, there was not a special IC for that purpose.
You will have to separate the "C" (color) component from the "VBS" (vdeo, blanking, sync).
Fortunately, that is relatively easy because the "C" component is a fixed-frequency carrier signal.
For NTSC, the FSCis 3.579545MHz, and for PAL, it is 4.43362MHz
So, if you want to boost the saturation, you simply amplify the color subcarrier before you re-insert it into the CVBS.
Your profile does not reveal where you are, but if you are in NTSC-land, you must be careful to avoid diddling the PHASE of the color subcarrier because that will affect the hue of the color. And even a slight change will produce a disturbing shift in color. But PAL is designed to be less sensitive since it reverses the phase of the FSC with every line.
Back in the day we used "processing amplifier" or "ProcAmp" gadgets. They would separately adjust all four parameters:
1) "Brightness" ("pedestal" in the video terms or "offset" in electronic terms.)
2) "Contrast" (luminance gain)
3) "Hue" (color subcarrier phase)
4) "Saturation" (color subcarrier amplitude/gain)
There are still NTSC and PAL proc-amps available on Ebay And maybe even some still available new.