Unless otherwise noted, the etymologies are sourced from the Oxford English Dictionary. Corrections are welcome.
Abenaki < French < Old Innu < Eastern Abenaki wαpánahki, lit. ‘dawn land’ (autonym)
Algonquin < 1600s French Algoumequin, possibly from Maliseet [ɛlægómogwik] ‘they are our relatives, allies’ (Day 1972)
Cheyenne < French < Dakota Šahi′yena
Chippewa < Ojibwe očipweː (autonym)
Cree < French < Old Algonquin kirištinō
Illinois < French < Illinois irenȣeȣa /irenweːwa/, lit. ‘s/he speaks the ordinary language’
Mahican < Munsee màːhíːkan < Mahican muhheakunneuw (autonym)
Maliseet < French < Mi’kmaq maliːsit, lit. ‘one who speaks poorly or incomprehensibly’
Massachusett < Massachusett Massachusêuck (autonym)
Menominee < Ojibwe manoːminiː ‘people of wild rice’
Meskwaki < Meskwaki meškwahkiːha ‘red earth person’ (autonym)
Mi’kmaq < French < Mi’kmaq miːkmaq ‘allies’ (autonym)
Miami < French < Illinois miamioua /myaːmiːwa/ ‘person from downstream’
Mohegan < Mohegan moyahegan, moya[u]hegunnewog ‘people of Mohegan’ (or ‘people of the hill-fort’, proposed by Ives Goddard in a presentation at the 46th Algonquian Conference)
Munsee < Munsee mə́n’siːw ‘person of Minisink Island’
Nanticoke < Powhatan Nautaquake, cf. Munsee wənéhtkoːw ‘Nanticoke person’
Naskapi < French < Innu unaskaːhpiːw
Ojibwe < Ojibwe očipweː (autonym)
Ottawa/Odawa < French outaouan < Ojibwe otaːwaː (autonym)
Passamaquoddy < Maliseet-Passamaquoddy pestəmohkatíyək, lit. ‘people from the place where pollock are plentiful’
Penobscot < Penobscot pɑnáwɑhpskek ‘where the rocks open out’
Peoria < French < Illinois peȣareȣa /peːwaːreːwa, peːwaːria/
Pequot < Narragansett pequttôog, perhaps lit. ‘people of the shoals’
Potawatomi < Ojibwe poːteːwaːtamiː
Sauk < French < Ojibwe osaːkiː, cf. Sauk asaːkiːwa ‘person of the outlet’
Shawnee < Munsee šawanow < Shawnee šawanoki ‘people of the south’