France, who lost their earlier finals in 1998 and 2012, will want it to be third time lucky as they face the top-seeded Polish duo of Agnieszka Radwanska and Grzegorz Panfil in the title match at the Perth Arena.
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.
Image: Alize Cornet and Jo-Wilfried Tsonga during the mixed doubles match against Anabel Medina Garrigues and Daniel Munoz-De La Nava of Spain on Day 7 of the Hopman Cup at Perth Arena, in Perth, Australia.
Photograph: Photo Will Russell/Getty Images