I want to replace 2 ceiling lights with 2 ceiling fans with light kits. The existing light fixtures are controlled by 1 on/off wall switch. From what I can see: the wall switch has 2 cables, 3 wires per cable, a black, white and ground wire. It seems the 1st ceiling light has a jumper cable to the next light. All I want to do is replace the lights with the ceiling fans. I don't know which wires to hook up, cable wires to fan wires.

Presumably at the switch the two white wires are connected together with a wire nut and the two black wires are connected to the switch.

If this is true you can install the fan/light but the switch will have to be on for anything to work. You can turn the fan or the light on or off with the pull chains but the switch must be on. The other way would be to use a remote to control the fan and lights but again the switch must be on.

To install the fan/light and use the pull chain;
The fan/light kit will have a black, a white and a blue (or a black with white stripe) wire. Connect the black and the blue wires to the black wire or wires in the ceiling.
Connect the white from the fan/light to the white wire or wires in the ceiling.
Connect the ground to the ground in the ceiling.

Does connecting two ceiling fans to one wall switch violates the electrical code?

No.