Needing a victory in their last group match, Cornet overcame a hamstring problem to trounce Anabel Medina Garrigues 6-2 6-2 before Tsonga defeated Daniel Munoz-De La Nava 6-4 6-7 (7) 6-2.
The French pair won the dead mixed doubles rubber 8-3.
Poland, making their Hopman Cup debut, confirmed their place in the final on Thursday after edging out Australia in their last match to finish above the Canadian pair of Eugenie Bouchard and Milos Raonic in group A.
(Writing by Sudipto Ganguly; editing by Pritha Sarkar)
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