PERTH, Australia (AFP) - A gallant Richard Gasquet led France to its second title at the mixed teams Hopman Cup in Perth on Saturday (Jan 7).

The 30-year-old gave the French the lead in the tie with a brave win in the singles, before dominating the deciding mixed doubles as he and Kristina Mladenovic beat the United States 2-1.

Twice American Jack Sock appeared to have Gasquet down for the count in the opening singles match of the final, but the world number 18 was able to dig deep and win in three sets.

After Gasquet's heroics, Coco Vandeweghe then beat Mladenovic in straight sets to level the tie.

The tournament came down to the mixed doubles, played under the Fast Four format, and both sides were unbeaten in the format going into the final.

However, it was Gasquet who again rose to the occasion with some brilliant shots as the French won 4-1, 4-3 (5/0).

It was France's second success at the Hopman Cup after Jo-Wilfried Tsonga and Alize Cornet won in 2014.

Gasquet said he and Mladenovic were an ideal pairing at the unique tournament.

"A lot of great players have won here, so that's why we're happy to have our names on the cup," he said.

"We are very proud, we are a very good team.

"That's why we won (doubles) four times in a row."

In a see-sawing men's singles match, the 30-year-old Gasquet seemed beaten when a double fault handed the 23rd-ranked Sock a break of serve to love for a 6-5 lead in the third set.

Sock thought he had finally cracked the match open, but Gasquet then returned the favour to break back to love and force a tie-breaker.

Gasquet raced to a 4-1 lead in the tie-breaker, but Sock then won four points in succession.

The American held match point in the tie-breaker, but it was Gasquet who converted his first chance for a 6-3, 5-7, 7-6 (8-6) win in two hours and 30 minutes.

The Frenchman said he simply tried to keep the pressure on Sock.

"Sometimes it is difficult to finish the match and it was for him," he said.

"I tried to concentrate on my return, not do any easy mistakes and make him play every point.

"It was a great match for me, after saving a match point I am really happy." The 36th-ranked Vandeweghe produced one of her best singles performances of the week to beat world number 43 Mladenovic in straight sets, 6-4, 7-5.

Vandeweghe showed improved consistency and the Frenchwoman was able to make little impression on the American's serve.

Mladenovic paid the price for being unable to convert some break points early in the second set, with the 25-year-old American producing a big forehand in the 11th game to secure the only break.

Vandeweghe then served it out to level the tie and set the scene for the mixed doubles decider.