The first French Mirage 2000 flew within 100ft of the BN2T Defender, which was on a solo navigation exercise to the north of Islay.
Aware that fast-jets normally operate in formations, the BN2T pilot continued to climb and soon spotted another Mirage which passed above him.
He assessed the risk of collision as medium.
The French jets were operating from RAF Leeming in Yorkshire as part of Exercise Joint Warrior in October last year. They did not report seeing the BN2T.
A report by the UK Airprox Board, which investigates near misses between aircraft, said: "Overall, this Airprox appears to have occurred due to ineffective lookout from the fast-jet captains and a decision by the BN2T captain to train in a height band routinely used by high-speed traffic."
The report found the BN2T pilot was receiving a basic service without the aid of surveillance equipment from Scottish flight information.
Just before the near miss he received a Traffic Alert & Collision Avoidance System (TCAS) alert warning him of an aircraft 100ft below him.
He climbed and rolled to the left and saw the Mirage pass around 200ft below him "at high speed".
The report praised his actions and said he had prevented the "close encounter" from becoming worse.
It said: "With regard to the BN2T's pilot, the board agreed that his actions following the TCAS alert showed commendable awareness in that, having climbed away from the threat and having seen the first Mirage, he continued searching for the second fast-jet even though he had no indication of its presence."
However the board found he might have been better avoiding the area or flying in a different altitude band due to the increase in low-level traffic during the exercise.
It also suggested it might have been better for him to obtain flight information from Scottish West Coast, which has radar coverage in the area, rather than Scottish Information.
The incident happened on October 10 last year.
The report concluded the cause of the Airprox was a "non-sighting by the Mirage 2000 pilots" and found that "whilst this was clearly a close encounter where safety margins had been much below the normal, the actions of the BN2T pilot had prevented it becoming worse".
It classed the degree of risk as "B", which means the safety of the aircraft may have been compromised.
The Airprox Board was also told that at the time of the Airprox, none of the pilots had access to the Centralised Aviation Data Service (CADS) which was still in its implementation phase.
CADS has now been fully implemented and has become a mandatory element of military flight planning. This means all military pilots now have access to each others' plans during their pre-flight preparations.