What should one do who missed the Fajr prayer on Friday, then caught the Imam in the first rak'ah of the Friday prayer; should he pray Fajr and complete Jumu'ah, or pray Jumu'ah and then make up Fajr?

You join the Imam with the intention of performing the Friday prayer, and then you pray Fajr after completing the Friday prayer. Here, disregarding the order of prayers is forgiven for one who feared missing the Friday prayer.