The article, which was adopted by a show of hands Tuesday night in the National Assembly, is the "cornerstone" of a law for "a state in the service of a trustworthy society", according to the government.
The law is part of reforms President Emmanuel Macron touted during his electoral campaign to allow citizens to make a mistake in good faith in their dealings with the authorities without risking punishment from the first infringement.
It will be up to the administration to prove that the person was acting in bad faith.
"The expansion of the right to make a mistake adopted by the Assembly just now!" minister of public action and accounts Gerald Darmanin said on Twitter.
"It is a revolution in the relations between the administration and the administered."
To err is human but the divine forgiveness of the government will be "limited to the first mistake", according to a change made to the article at the insistence of dissenters.
At the opening of debate, the minister said the government had listened to "the French who like their public services but not their administration", citing a letter of grievances sent him by one "Alexandre".
Lawmakers will have to consider dozens of further articles in the bill on the extent of the right to make mistakes.
The right to err will not apply in a number of cases, such as public health.
Considered a "catch-all" by some officials, the bill deals with subjects as diverse as modifying procedures for obtaining a permit for the installation of wind farms at sea or the possibility of making donations to churches by SMS.