There is a good Wikipedia article on Métis here:
https://en.wikipedia.org/wiki/M%C3%A9tis
Follow the links to both the Canadian and American Metis.
There is currently a great deal of political dispute in Canada about the term Métis. Métis simply means "mixed" in French and is the same word as Mestizo. In France, métis, would generally be understood to mean mulatto. In North America it was the general term for those of mixed European and First Nations or Native American heritage, especially those of the French fur trading era. From at least the mid 1700s on, the large extended kinship networks of those mixed heritage families gave rise to a separate people who intermarried with European settlers, with Native Americans and with each other. Legally though, there are varying circumstances. In the U.S., Metis were not recognized as a separate people. Instead, some are included among the Chippewa Tribes especially Turtle Mountain and others among those with "Canadien" ancestry in and around Michigan and Wisconsin. Not being included on Indian rolls had an advantage in the U.S.: Indians were not allowed to own land at the time, only live on lands reserved for them... The U.S. Chippewa communities are closely tied to the Canadian Red River Metis and the Ojibwe and Metis of Ontario.
In Canada, Metis around the Red River were given Scrip for land allowance after the failed Red River Rebellion. Other Metis were not. Both groups suffered privation at the hands of Canadian settlers, but those in the West also suffered the consequences of military defeat. There is now a HOTLY contested debate about who in Canada has the right to be called Metis. Much like the effects of Federal recognition on tribes in the U.S. and the debates about who or who is not allowed on tribal rolls, it is a FOLLOW THE MONEY kind of story and largely not a debate about genealogy or cultural heritage but of determining the community right to compensation and a piece of the pie. There are prominent organizations promoting a coast to coast vision of Metis which include Metis civil rights notables and scholars pitted against groups centered on a Red River and western Ontario only vision who have more engagement from government at the federal level. (Members of both camps were Intervenors in the Daniels case which is the Canadian supreme court case which determined that both non-status Indians and Métis were "Indians" under Canadian Federal law and that it was a Federal rather than Provincial responsibility to engage.
All these groups will have differing criteria regarding who is or is not Metis. Those centered on Red River will want proof that an ancestor received Scrip or was listed as half-breed on a Canadian census in the west after the 1750s. Other groups will want genealogical proof of a tie to any Metis family proper or even occasionally only require a single aboriginal ancestor if the person is engaged in cultural activities. In the U.S., it could mean French Metis ancestry with or without tribal enrollment with the Chippewa.
I know that's a long answer, but it's a complicated issue. In general, look to descendants of the Fur Trade. Especially if the fathers were Voyageurs. Voyageur contracts can be searched here:
http://shsb.mb.ca/en/Voyageurs_database