A special election will be held in November for the final two years of Franken's term, a race Smith said she plans to enter. The election for the seat's full six-year term will take place in 2020.
Jones won last month's special election in Alabama by a slim margin against Republican Roy Moore. Sen. Luther Strange was appointed to hold the seat after former Sen. Jeff Sessions became attorney general.
Alabama's state canvassing board certified Jones last week as winner of the special election, despite Moore filing a lawsuit contesting those results claiming election fraud.