(Read more: Euro zone business activity strongest in 32 months)
The Purchasing Managers Index for the euro area as a whole came in at 53.2, only a fraction down from last month's reading of 53.3. The stabilization of the job market contrasted markedly with the steep rate of job losses this time last year.
The largest gain in backlogs of work in France since August 2011 suggests employment could start rising again in the country in April and the rate of job losses, which eased in March, showed a near-stabilization of the French job market, chief economist at Markit, Chris Williamson said.
Germany, in contrast, saw output growth slow to a four-month low, easing in both manufacturing and services. The rate of expansion nonetheless remained solid, said Williamson, finishing off the best quarter of growth since the second quarter of 2011.
"Germany looks set to have grown by 0.7 percent in the first three months of the year, spearheading the region‟s upturn despite its PMI slipping lower in March. However, perhaps the best news this month is the sign of the region‟s upturn spreading to France," he said.
(Read more: European markets turn lower, German PMI disappoints)
German business activity fell from the 33- month high reached in February to a reading of 55.0 in March. Companies in the goods producing sector reported the slowest rise in output since November and the private sector reported a moderation in growth of incoming new business.