“Je m’en fais la répétition” here simply means “I repeat them”. “En“, standing for “the words”. The construction of the sentence is akward in French, as is in fact all that Catherine says in French in the play. Nobody would speak like Shakespeare has Catherine speak in the play. I expect it is as much because French has changed since the 16th century and because most probably Shakespeare’s French wasn’t that good, even for the times’ standards.

“Je m’en fais“, when not followed by an object, means “I worry”. It is a reflexive verb.
Not to be confused with e.g.: “Je m’en fais une montagne” meaning “I do make a big deal out of it”.