Dan Gamble, the tighthead prop, and Roan Frostwick, the scrum-half, have been drafted in for the match at the DAM Health Stadium on Friday night.
Edinburgh had vacancies in their squad after deregistering George Taylor, who was forced to retire in January due to a history of head injuries, and Jordan Venter, who left the club to join Bath in December.
Gamble, from Kelso, is a Scotland Under-20 international who came through the Edinburgh Rugby Academy and was loaned out to London Scottish in January.
Frostwick, a product of North Berwick RFC, is also a Scotland U20 cap and had a spell on loan at English Championship side Ampthill.
Friday’s match against Pau is Edinburgh’s last in Pool C of the Challenge Cup and a win will see them top the group and have a home tie in the last 16, most likely against Bath.