France won the opening singles when Jo-Wilfried Tsonga overwhelmed Isner 6-3, 6-2. Williams then tied it after trailing by a set and 4-1 to defeat Mathilde Johansson 3-6, 7-5, 6-4. The Americans won the mixed doubles 6-7 (5), 6-2 10-8 by taking six of the last seven points in the match tiebreaker.
The U.S., which defeated South Africa in its opening series, next plays Spain.
Williams played listlessly before recovering. After making the only break of the final set to lead 4-3 she faced two break points in the following game before holding for 5-3. She would not elaborate on her obvious discomfort.
"I'm OK, thank you; I'm OK," she said. "She hits the ball hard and low and I'm tall so it was hard to get down that low all the time. I have to give her a lot of credit for a tough match."
Tsonga gave up just seven points on serve and committed only four unforced errors against 21 from Isner to win easily.
"It's never easy against John usually, so I'm really happy with the way I played today," said Tsonga, who had lost three of his previous four matches against the American. "It's a really good start for 2013 and I hope I will have some more like this. I was a bit quicker on court than before so I think it's a good sign for the rest of the competition and for Melbourne."
The Australian Open begins in Melbourne on Jan. 14.
Isner's right knee was wrapped because of what he said was "a little tendinitis." He said he was not concerned at losing both his singles so far at the Hopman Cup.
"Normally, it takes me a while to get going," he said. "I'm not worried about it though. I remember three years ago when I first played this event I didn't play so well here but I won the next tournament.
"It certainly wasn't my best. I was missing shots I would have liked to have made. I'm not freaking out about it."
On Wednesday, Italy plays Germany and Australia faces Serbia.