In French, the noun protégé has aigu accents over both e‘s. In English, some writers and publishers preserve the French accents, but English is not kind to these marks. They are often omitted in informal writing, and they are increasingly omitted in edited writing. Unlike résumé, which when unaccented can be confused with the verb resume, protégé does not have an unaccented homograph with which it may be confused. So dropping the accents does not create ambiguity.
Examples
Some major publications use the accents—for example:
Kennedy lobbied for his longtime protégé. [USA Today]
His beloved protégé has found a new benefactor. [Independent]
Foy did this politely, of course, since Weber is a scholar at Stanford with a towering reputation as Mà¼ller’s protégé. [Vancouver Sun]
And some don’t use the accents—for example:
Last week Blumenthal launched a search for a new protege. [New Zealand Herald]
A protege of the late Jack Kemp, Ryan has long concerned himself with applying conservative principles … [Politico]
… his protege was appointed to replace him at the head of the fashion house. [Guardian]

