The English word “penance” comes from the Latin word for repentance.
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Maybe so, but there’s still a problem with the Latin.
In the Greek and Hebrew, the concept of repentance is an internal change, or a turning back, or sorrow for sin. Usually all of the above.
But when translated into Latin, it somehow turned from an internal change to having to do external works, which is not what the original languages say.
I don’t think the Latin points that out specifically. The root of “pænitentia” certainly indicates one who is sorrowful, thus pointing to an internal change.
Remember also that John the Baptist warned the Jewish priesthood to “bring forth fruits worthy for repentance” (Matthew 3:8, Luke 3:8). This is a different word from the Greek word translated “works” in James 2 (which is “erga”; also used in Revelation 2), but certainly one must work to produce such fruit.