Make some sense. First (obviously) because of F-104J having it. And the competing Phantom that carried the day.
But there is more. According to Liébert & Buyck landmark book, J79-powered Mirage F1s were being considering the same year, 1968. For the French Navy (from memory) because the Aéronavale had very stringent loiter and climb requirements for an interceptor to replace the Crusaders.
Basic navalized F1 with Atar 9K50 would be hopeless, so they were considering M53-2 (not ready until 1973 at the earliest) - so Spey and J79s were also contenders.
TF306E, as flown at the time on the Mirage F2 and its close sibling the Mirage G, would not fit into a F1.