There are several options for put ins for rafting. One thing to consider is that there are brush and tree hazards because there is not high water levels. If you are rafting for the first time you may get pushed into trees or brush.
One put in option is Friant Bridge which is at an elevation of approximately 315. It is next to the bridge. The trick is that just afting put in you will need to paddle to get through remains of an old bridge. It also can be tough when water levels are high thus is not as frequently used as other options.
The next option is Lost Lake County Park . This is great because you can practice and paddle around a bit before real rafting to get your bearing.
The First Mansion rafting put in option is challenging because at this point it splits into 3 channels. One is very narrow and has bends. The other splits to the Cobb channel. The middle one is most open and straight.
The Donaghy Mansion option is near some heron and egret nest areas.
The Causeway Culvert one requires rafting with a bit of still. You need to paddle through a culvert or carry your canoe up a steep bank and over a road and then put it back in at the other side just a bit after put in.
Fort Washing Beach rafting put in is privately owned so there is a charge for parking.
The Highway 41 Bridge may be a bit uncomfortable for some because below the bridge the river flows through narrow channels.
Sycamore Island is a nice one exact just after put in the river narrows and rafting participants need to watch for low hanging trees.
Scout Island put in is a Fresno County School owned site so it typically is not open to the public.