Debutant Corentin Moutet gave 10-time champions France the ideal start in Osijek by beating home favourite Dino Prizmic 6-4 5-7 6-1 on Friday before world No.57 Arthur Rinderknech topped big-serving 2014 US Open winner Marin Cilic 6-4 6-4.
France will progress if they win any of the possible three rubbers on Saturday, beginning with the doubles.
In Groningen, hosts the Netherlands are hoping to emulate last year's run to the final, which they lost to Italy, but already have a mountain to climb after losing both singles to Argentina.
Jesper De Jong was beaten 6-4 6-4 by Tomas Etcheverry before world No.21 Francisco Cerundolo battled past Botic van de Zandschulp 7-6 (7-1) 6-1 to put the visitors in charge.
Dutch captain Paul Haarhuis said his side will need to be perfect on Saturday.
"We can't afford any bad matches tomorrow, it's a deep hole we're in," he said.
"But we still have a chance."
Austria are well-placed to spring a surprise in Hungary after also moving 2-0 ahead in Debrecen.
Jurij Rodionov, ranked 158th in the world, gave Austria the lead by stunning 56th-ranked Fabian Marozsan 6-2 6-7 (5-7) 7-5 and Lukas Neumayer then, also ranked outside the top 50, outlasted the experienced Marton Fucsovics 6-3 3-6 7-6 (9-7).
Germany's Jan-Lennard Struff, who reached the fourth round at Flushing Meadows this month, put his side ahead against Japan in Tokyo with a hard-fought three-set win against Yoshihito Nishioka and Yannick Hanfmann eased past Shintaro Mochizuki.
The United States are playing a strong Czech Republic in Delray Beach while Spain's clash with Denmark in Marbella begins on Saturday, as does Australia's home tie with Belgium.
Holders Italy are through to the Final 8 as hosts with the seven winners from this weekend's qualifiers joining them.
