Net profit rose by 22.0% to 1.19 billion euros ($1.63 billion), above analysts forecasts, after a record business year driven by strong demand for engines for airliners.
Operating profit rose by 23.8%, and the margin rose to 12.2% of sales from 10.8% in 2012.
Safran said it expected a further rise in operating profit this year of slightly more than 10.0%.
Safran shares were down 2.17% to 52.35 euros in an overall market down 0.14% in afternoon trading.
At Global Equities, broker Yves Marcais said, "The figures are very good, but people are selling on the news: They are taking profits because the announcements had been anticipated and had already pushed up the price."
CEO Jean-Paul Herteman said that the group was "particularly confident" about raising results again this year.
Safran took a record high volume of orders totalling 20.8 billion euros last year, pushing the total order book to 56.2 billion euros.
CFM International which it owns together with U.S. group General Electric (IW 500/6), turned out a record number of 1,502 CFM56 engines last year.
World's Top Seller
This is the most sold aero engine in the world, and the company has orders for 5,000 more.
The order book for the successor engine, the Leap, which will power most new medium-haul airliners, totals more than 5,700 engines representing nearly four years of production.
In dollar terms, activities for servicing civil aero engines rose by 19.2%. This was partly because U.S. airlines were catching up on maintenance which had been delayed during two or three difficult years, Herteman said.
This process of catching up would be spread over several years, he said.
Safran also makes engines for the Ariane space rocket.
However, aero equipment activities drove growth since defence and safety activities each fell by 2.8%.
Western military defense budgets are being cut back, but Safran is maintaining investment out of shareholders' funds in order to remain "a world-class player," Herteman said.
This investment also had benefits for the civil sector and for growing export markets, he said.
Copyright Agence France-Presse, 2014