If you're going to do a clean sheet design to replace the A340-300 the economics greatly favor a twin engine configuration. That's what Airbus chose for the A340-300 replacement - the A350-800.
If you are only considering retrofit of the existing CFM56-5C3 engine with a geared fan engine of similar thrust that is already under development, such as the PW1133G, as a minimum it would require new nacelles/pylons. And would likely require taller landing gear, since the fan of the PW1133G is about 20 inches larger in diameter than the CFM56-5C3 fan.
In reality, the cost to re-engine the A340-300 would not likely be viable given the relatively small number of this aircraft model in service. However, the much greater bypass ratio (12.5:1 vs 5.5:1) and overall pressure ratio (50:1 vs 33:1) of the new PW1133G vs the legacy CFM56-5C3 would definitely result in significantly lower fuel consumption.
Interesting question from a technical perspective, but ultimately the decision is driven mostly by economic factors.