this market is basically two horse race. Rolls Royce and General Electrics. why Safran didn't enter in this field in 70's just like other players as they could have won some contracts from Airbus.
maybe they didn't have technology back then.
Both China and Russia recently build open air bench test facility for large turbofan engines. PD-35/CJ-2000.. its a historical shift from western led large aviation Engines industry. not saying they will compete with them but at least both can capture their domestic markets.