You should bring a collapsible saw and a small hatchet. Once you get to your site you would look for dead wood on the ground in the forest and chop it up as needed! You should try to have a small, cherry fire rather than a roaring blaze so that you don’t use up all the wood at a site. If the site is heavily used or on an island you can paddle to another area of the lake and fill your canoe up w wood to bring back. Hope that helps! 

Collapsible saw is great, Those little hand ones are a pain in the ….. and it takes a lot of work even on a small log.  Small sticks okay,  As for a hatchette there is more chance you will injure yourself, especially if you are not familiar with chopping.  For my back woods canoe trips I have a 2.5 lbs. head with a 24″ handle.  There are a variety of prices for saws, middle of the road is fine.