I don’t know how much a video tutorial would help you. If I’m honest, I see little value in watching someone else draw. Much better to just get into drawing the characters yourself, and practising the style.
It is entirely possible to get that hand drawn, and hand coloured look in Adobe Illustrator. However, you are probably going to need a graphics tablet to do it. I couldn’t imagine doing this with a mouse. The graphics tablet I use is one of the cheaper Wacom Bamboo tablets.
What I suggest you do is download some Asterix images, and try drawing some of the characters yourself, so you can get a feel for the style. Use the comic image for tracing over with ink lines.
Set up layers in your Illustrator document with one layer for the ink, one for the colour, and one for the image to be traced. Set your brush tool to a small size, and switch on the pressure sensitivity for the size, so that you can get variable width strokes.
Later when you want to try your own creations, perhaps create a separate layer for your rough sketch. Then you can simply switch it off after you have drawn better quality ink lines on the ink layer.
My example here is a bit wonky, but I think I quite like it that way – the less than perfect look gives it that hand drawn feel. I’m pretty sure with a bit more care you could get better results. Also, I am no cartoonist, so I’m already at a disadvantage there.
My attempt is the one on the left. You can also see my layers arrangement – one for the ink, and the colour layer under that.