>>1164968A300 did have the range for transatlantic flights and flights to the Middle East from Europe. The A330 fills a similar role, though its range is larger and enables it to serve even longer routes, but with higher capacity.
I do know about the A340 and the A330 being developed at the same time, but the idea behind the A340 was taking the basic fusilage and systems from the A330, giving it 4 narrow body engines, and stretching the aircraft to have more seats, and have more space for fuel, thus allowing longer ranges.
Dual aisle short haul is a non-existant market, outside of some weird applications. British Airways does use the B767 for several domestic flights in the UK, but that is also for the movement of large aircraft from airports like Manchester to Heathrow. Lufthansa does use the A340 to avoid issues with overbooking inside Europe.
Problem the A300 had in Europe was that the B737 and other single aisles like the BAC One-Eleven were more popular for short haul. That's what lead Airbus to developing the A320.