United States on top in Davis Cup opener against Uzbekistan
McDonald, who knocked Rafael Nadal out of the Australian Open last month, eased past Sergey Fomin 6-4, 6-1 in Tashkent before Tommy Paul, a semi-finalist at the season-opening Grand Slam in Melbourne, defeated Khumoyun Sultanov 6-1, 7-6 (8/6).
France, the 10-time champions, were 1-1 against Hungary in Tatabanya.
World number 182 Zsombor Piros stunned 45th-ranked Benjamin Bonzi 7-6 (7/4), 6-3 before Ugo Humbert levelled the qualifier by seeing off Marton Fucsovics 6-3, 6-2.
"It was my first match in the Davis Cup and I was very excited," said 24-year-old Humbert, the world number 86.
"I tried to stay focussed on what I was doing and it went well."
There are 12 ties taking place this weekend with the winners securing places in the group stage in September alongside defending champions Canada, 2022 runners-up Australia and wild cards Italy and Spain.
The eight best teams then go through to the Davis Cup Finals knockout stage in Malaga in November.
The qualifying matches taking place between Friday and Sunday are the first since the International Tennis Federation severed its controversial partnership with investors Kosmos less than five years after a 25-year deal was signed.