You can charge using AC at as little as 6 amps and (for most cars) as little as 100 volts, so, with carefully adjusted parameters and a bit of custom electronics in the EVSE controller, a 600 W generator could just about charge a car. But that would be really slow: most cars use 200 to 300 W just to run their own electronics, so only a useful 300 W or so would charge the battery, about 1 mile range regained per hour.
A building-site frame generator could put out close to the 7 kW maximum for 230 V 32 A charging, about 20 miles/hour, but it would fill your entire car boot and be too heavy to lift out to run. Might be an option for a breakdown van, but a trailer or dolly to tow the car to the nearest rapid charger, would be simpler.
With that said, I'll add my recommendation just not to run out of charge. In England, you'll rarely be more than 15 miles from the nearest rapid charger, although it might not be one you would normally approve of. More careful planning needed in Scotland or Wales. If you include public AC chargers, rarely more than 10 miles away. If you realise that you don't have enough range even for that, slow down (and turn off the aircon and heating)! Most EVs are at their most efficient at about 20 mph (30 km/h). Slowing right down may increase your range enough to avoid running out completely.
(My van-based car with the aerodynamics of a haystack returns better than 5 miles/kWh at 20 to 30 mph, about double its efficiency at 70. Even slowing down to 50 if you are worried about reaching the next motorway services can really help.)
If I drove with a 75 mile reserve, I'd have to charge every 15 miles or so. That advice isn't practical for me. On long journeys I'm happy to arrive at a planned charging stop with just enough range left to be sure of a plan B, so long as plan A was for a multi-charger site of a reliable brand.
