The unexepected rise in the indicator still leaves it below the long-term average fixed at 100 points.
The key industrial confidence index rose three points to 96 points, while analysts and economists surveyed by Dow Jones Newswires had expected it to come in at 93 points.
The sentiment concerning demand and total order levels improved by three points, while that for exports jumped by 18 points, but both remained sharply negative.
"Looking at the personal production outlook, which improves markedly, activity in manufacturing industry would be more dynamic in the next months," said INSEE.
"The general production outlook, which represents business leaders' opinion on French industry as a whole, improves strongly but are always below its long-term average," it added.
The general production expectations for industry rose by 17 points to -15.
The index for the services sector rose two points in March to 93 points, while that for retail trade climbed by three points to 94 points.
The construction index dipped one point to 98, while the wholesale trade index came in at 100.
Another key leading indicator, the Purchasing Managers' Index compiled by the Markit research firm, fell in March to 49.0 points from 50.2 points in February however.