Best Time to GRAFT a peach Branch?
Not a good idea. On a tree of that age, the graft is less likely to take. And in the first place, to graft successfully you have to really know what you are doing and practice rigorous good hygiene whilst doing it, disinfecting everything as you go, or else it won't succeed. And even if they do take, they will take several years before they bear fruit. You are far better off either encouraging it to grow more stems on that side through strategic pruning, or else training some stems from the middle of the tree over to that side by using sticks and wires.
You can train the branches to other side with the help of copper wire, that will be easiest way. If you want to propagate the tree then Air layering is best way, winter to summer time is suitable for this for air layering see this video https://www.youtube.com/watch?v=TgKrIelx6WI