Sergey Kisliak scored the only goal four minutes from time to punish France, who failed to capitalise after dominating possession.
Blanc retained six of the side who lost to Norway in a friendly last month, including centre-halves Adil Rami and Philippe Mexes and front three Jeremy Menez, Guillaume Hoarau and Loic Remy.
Aleksandr Kulchy had the first chance for the visitors when he met Alexander Yurevich's cross but Rami stood firm to block.
Alexander Hleb saw an effort blocked by former Arsenal team-mate Bacary Sagna before France again pressed forward. New captain Florent Malouda was off target with an acrobatic effort before Hoarau also fired wide.
Mathieu Valbuena, on as a substitute for the injured Remy, almost made an immediate and spectacular impact but his volley was blocked by Yurevich, who had similarly thwarted Malouda moments earlier.
Malouda's 25-yard drive then caused problems for keeper Yuri Zhevnov, who kept his concentration to beat away the viciously swerving shot and ensure half-time arrived with no score.
France started the second half brightly and Menez and M'Vila forced good saves from Zhevnov either side of a glaring miss from Hoarau. The Reunion-born striker was picked out by Menez's cut-back but, leaning back and under pressure, spooned his effort high over the bar.
On a rare Belarus break, Vitaly Rodionov shot narrowly wide, but the hosts soon regained the initiative and Malouda's diving header was saved after Hoarau flicked on Sagna's long throw.
A bout of head tennis ended with Hoarau nodding over the bar, and Malouda then had the ball in the net but was correctly flagged offside.
Zhevnov tipped Valbuena's drive over before Louis Saha, a substitute for Menez, was himself withdrawn due to injury after just 10 minutes on the pitch.
Having failed to make their dominance pay, though, France were caught by a sting in the tail largely of their own making.
A mix-up between M'Vila and Gael Clichy allowed Vyacheslav Hleb to bundle his way through the defence and pull the ball back for Kisliak to finish powerfully into the top corner from 12 yards.
France had a last-gasp chance to salvage a point as debutant substitute Kevin Gameiro lashed a volley on the turn inches over the crossbar following a corner.
France next face a difficult trip on Tuesday to Bosnia and Herzegovina, who tonight won 3-0 in Luxembourg.