France, who beat Australia in the last final of the 57-year-old team event's previous format in November, are one of four nations who qualified automatically for the 12-nation event to be staged on clay at the Laszlo Papp Sports Arena.
Hungary, as hosts, Australia as runners-up and 11-times winners Czech Republic, as a wild card, were the other three.
Tuesday's draw held in Budapest's majestic Museum of Fine Arts paired record 18-times Fed Cup champions United States with Slovakia and five-times winners Spain who will fancy their chances on their favoured red dust.
Last year's runners-up Australia face Belgium and surprise finalists Belarus in Group B.
Czech Republic face Germany and Switzerland in Group D.
The four group winners will go through to the semi-finals followed by a final. Individual ties will consist of two singles matches followed by a doubles.
The Fed Cup's new format, which saw eight nations qualify through playoffs last weekend, is something of a throwback to the first edition in 1963 when 16 nations played over a week at London's Queen's Club with United States, featuring Billie Jean King, beating Australia in the final.
King was present at the draw ceremony and praised the International Tennis Federation's elevation of the women's team event which now shares equal prize money with the Davis Cup.
The competing players at the week-long event will split $12 million with the other $6 million going to federations.
"Women's tennis has always been the leader in women's sport," American King, the trailblazer and inspiration behind the formation of the WTA Tour, said at the draw ceremony.
This sends a very strong message. I'm very excited and really want to thank Hungary and everyone involved. This is an amazing opportunity.
While the change of the men's Davis Cup from a year-long 'home-away' World Group knockout draw to a one-week showdown in Madrid suffered some teething problems, the new Fed Cup format has been greeted in generally positive fashion.
The April slot is a much better fit than the men's Davis Cup which was played with 18 nations and crammed into a week in November, including gruelling late-night finishes.
FED CUP DRAW
France, Hungary, Russia
Australia, Belgium, Belarus
United States, Slovakia, Spain
Czech Rep, Germany, Switzerland