Lurching forward in first gear

Your car isn't getting enough fuel, you're not supposed to be driving along without your foot on the throttle in any gear really. Higher gears have less torque and actually demand less fuel to coast.

 

It’s not a clear description for us to go on but the clutch is snappy and first gear is relatively short. If you’ve got the 1300 cc version, there’s a decent amount of torque so it may be the cause. You sort of get used to driving the Copen (to the extent I’m a complete klutz driving the wife’s Mazda).

If you’re concerned, get the gearbox oil changed. It should be done at 8 years on the 1300 cc and is relatively cheap. The transmission oil spec is in the manual.

 

It's not a problem with your car.
Your car is lurching because it's not getting enough petrol to run smoothly.
Diesels generally have more torque than petrol, more pulling power, that's why it's used for lorries and wagons that move at relatively low speeds pulling heavy loads, so at low fuel and presumably with a bigger engine, the diesel still has enough power to pull itself forward smoothly. A 659cc petrol car needs a bit of gas.

All cars are slightly different, in fuel settings, clutch biting points ect, once you've been driving for a few years and in a few different cars you learn to adjust fairly quickly, unless you get some really horrible courtesy car like a Nissan Quashqai and feel like you're driving a bus for 3 weeks.

 

Age and engine temperature affect it too - more modern cars have better fuel control and are less likely to stall, which is what your copen is coming close to when it's jerking like that.
My first car had a manual choke, when you first started the car you had to pull the choke out to let more petrol in, then gradually push it back in to reduce the flow as the engine warmed up. If you didn't pull it out or pushed it in too soon, the car would judder like yours even with throttle!