That’s an interesting question. I assume they are new boards, recently purchased and left over from your fencing project. They are probably not weathered.
Modern chemicals and methods are safer than older methods. That doesn’t mean there is absolutely no risk, just not as much risk. Don’t stick your fingers in your eyes after handling it. Be careful breathing sawdust. Things like that. Just reasonable precautions you should take anyway. Anything that touches the ground should be treated wood or one of those really expensive types of wood that resists rot and termites.
If the wood is dried, you should be fine. If it is still really fresh it could be a bit more of a problem since it might give off fumes as it dries. If you do use it to build your coop and it is fresh, I’d suggest you do as Chris suggested and paint the inside. If it’s not real fresh, you should not need to paint it. Painting the outside is a pure personal choice. Fumes won’t build up out there. In any case, make sure you have good ventilation in your coop, which you should have anyway for many other reasons than treated wood.
If I had treated wood left over from another project I’d use it. That’s called recycling. Helps your pocketbook and is good for the environment.