Seventh-seeded Tsonga accounted for another French player, ninth seed Richard Gasquet 6-4 3-6 6-3 6-2 in a fourth-round clash.
Tsonga will play the winner of the match between Roger Federer and young Canadian Milos Raonic.
Earlier, Chardy won through to his first grand slam quarter-final after beating Italian Andreas Seppi.
Chardy booked a berth in the final eight with a 5-7 6-3 6-2 6-2 win over the 21st seed.
In five previous appearances at Melbourne Park, he'd never made it further than the second round, with his former best grand slam effort the fourth round at the French Open back in 2008.
The world No.36 will play the winner of the fourth-round meeting between third seed Andy Murray and another Frenchman, 14th seed Gilles Simon.