The Real Sociedad forward, winning only his third cap, looked to have secured a fourth successive victory for France with an 82nd-minute strike in Nice.
However, there was still time for Paraguay to level through a header from captain Victor Caceres, denying Didier Deschamps' men another success ahead of the FIFA World Cup.
Remy's first sight of goal came as early as the fourth minute but it was a neat link-up with Giroud in the 18th minute that nearly brought a first-half opener.
Paul Pogba shone in midfield for France as they dominated proceedings, and the 21-year-old sent two low shots fizzing wide of Antony Silva's goal.
The keeper's ball found Giroud on the right and, after beating two defenders, the striker played a cross into Remy, whose acrobatic effort flew agonisingly wide.
Paraguay started the second half with renewed impetus and brought the first save of note out of Lloris after Bacary Sagna had brought down Caceres, the Tottenham keeper getting down well to save Miguel Samudio's free-kick.
With time running out France, who sorely missed Ribery's creativity, continued to apply pressure and were finally rewarded as Griezmann fired home after Silva had saved well from Giroud.
However, the hosts were denied victory when Caceres met Jorge Rojas' cross, although Lloris may feel he could have done better.
