The fuel engine would be very small and weak, it would slide out of the car easily and the fuel tank would sit on top of the engine so it wouldn't need a fuel pump, gravity would pull the fuel into the engine as the throttle opens. There would only be two connections between the fuel engine and the car, a fuel line and power out socket, that's it. It would be bolted down in the bonnet just like a harddisk on a desktop computer.
The batteries would be very strong but they would only store enough power to take the car 20 kilometres. When the car is parked, the fuel and electric engine would both be switched off but sunlight would help to finish recharging the batteries through the solar panel that is integrated into the roof.
If you wanted to go more than 20 kilometres it would be fine because the small fuel engine and solar panels would help to top up the charge and slow down the charge depletion.
The electric motor wouldn't work very hard because there are no excess parts, the car wouldn't weigh much, there would be no exhaust pipe, no clutch, no gears, the fuel engine would weigh as much as a lawnmower engine, about 8 killograms and the electric motor would weigh the same.
That is the way I think. It is not necessary right or wrong, just a thought that may never get beyond this blog.