Low carbon steels will in general be more flexible than steels with higher carbon contents so yes, you're probably thinking along the right lines for a thin blade that might not snap so easily. And you can get one from France for a fiver.
A carbon content in the region of 0.5% tends to be used more in machinery than in knife blades, although a lot of kitchen knives and I believe the famous Opinel carbon blades use steel with about 0.4% carbon.
But there's a lot more to using a steel than knowing how much carbon is in it.
The presence or absebce of elements like chromium, copper, molybdenum, nickel and vanadium are especially important, as can be the absence of elements like nitrogen, sulphur and (shudder) hydrogen.
Depending on the application, phosphorous can be a very good thing in very small quantites and a very bad thing in less small (but still small) quantites. Some applications can forgive much larger quantities of elements like aluminium, lead and silicon.
The steels used in knife blades are invariably heat treated, and this treatment is often much more important than the precise composition of the blade.
All steels corrode. Some corrode a lot more quickly in some conditions than other steels will do in the same conditions.
Steels can be work-hardened. That may be a good thing or it may not, and the composition may encourage or discourage it.
There are many steels which are available very cheaply (and even for nothing) which will make excellent knives. I have some really lovely parangs which were made in Malaysia from old truck springs, but if you don't get the contact quite right with a big chopping move they don't half give the palm of your hand a slap!
A lot of people who make knives rarely use anything but O1 tool steel, it's a time-honoured and well-known material. A number of my blades are made from O1, which is cheap compared with the various stainless steels in most of my smaller blades. I don't mind hacking firewood that might have the odd surprise in it with a cheap blade, about the worst that can happen is that I'll have to grind a ding out of it.
A lot of people pick up old files at car boot sales. Anybody's guess what they're made of half the time, but some have made lovely-looking and apparently perfectly serviceable knives with them. Again, heat treatment is the key.
Do you have a big pile of steel sitting somewhere and you're wondering what to do with it?