When the word savage entered English in the thirteenth century, it was in the adjectival form. Savage as a person goes back to the fifteenth century (and emerged from the former), and the verb to savage is from the nineteenth century. All of these forms go back to the French word sauvage, which earlier on took the form salvage (different origin than the English word; I checked). This meant "untamed", much as today, and hails from its Latin cognate salvaticus, which is a slight modification of the earlier term silvaticus, which figuratively meant "wild" and literally means "of the woods" (that connection is clear), from silva, "forest". This goes back to the Proto-Indo-European reconstructed root sel, which meant "frame", "board", and had several other wooden connotations as well. Unironically, as society has grown more modern since the 1800s, the word savage lost usage.
Adam Aleksic, a rising sophomore studying linguistics and government at Harvard University, has been described as the internet's sixth most famous etymologist. He also has disturbing interests in politics, vexillology, geography, board games, conlanging, and law.