How to make carbon fiber composite more flexuraly strong?

I could be wrong, but I believe that carbon fiber composite is relatively brittle, i.e you don’t have to bend it very far before breakage. Since carbon fabric is obviously very flexible, I presume that the resin component is what gives the composite its inflexibility. So what can you change to make the composite more flexible, for example if you wanted to make a leaf spring?

You are correct – in general carbon fiber materials are not well suited for making a spring. But to make one, you would probably use a more flexible plastic at the core, then reinforce it with carbon/epoxy.

Prosthetic limbs use carbon fiber leaf springs already.

The auto-industry is already using composite leaf springs made from fiber glass. Composite leaf springs made from carbon fibers are even lighter than the fiber glass ones, but cost more and are not as strong as the fiber glass ones.