If he knows that he is offering the eclipse prayer, then he should not join him, because of the difference in nature between the two prayers. Although the eclipse prayer is two rak'ahs, each rak’ah includes two bowings, two standings and two recitations. So whoever does not realize that the imam is offering the eclipse prayers and join the imam with the intention of praying Fajr should form the intention of praying separately from the imam when he realizes that the imam is offering the eclipse prayer. Then he should complete his prayer as Fajr and then if he wants he may join the imam for whatever is left of the eclipse prayer.
And Allaah is the Source of strength.