The airline posted a better-than-expected operating profit of €816m (£613m), compared with a €129m loss for 2014.
The results sent shares up more than 10% to €8.22 in late trading in Paris.
However, the company warned that lower ticket prices would erode the benefits of cheaper fuel this year.
"The global context in 2016 remains highly uncertain regarding fuel prices, the continuation of the overcapacity situation on several markets, and the geopolitical and economic context in which we operate," Air France-KLM said.
Cheaper oil reduced the annual fuel bill by 6.7% to €6.18bn, with a 20% fall in the fourth quarter, although existing hedging contracts limited some of the savings.
The November terror attacks in Paris cut revenue by an estimated €120m in the fourth quarter as tourists stayed away from the French capital.
Despite the attacks, revenue for the three months to 31 December rose 2.2% to €6.3bn.
The airline is cutting labour costs and restructuring its network to compete with fast-growing Gulf airlines and European low-cost carriers.
Air France-KLM lowered net debt by €1.1bn to €4.3bn and pledged to reduce the figure further this year.
Chief executive Alexandre de Juniac said the company continued to negotiate new agreements with staff to improve its competitiveness.
Last year, the airline was embroiled in often bitter talks with staff as it sought to impose its "Perform 2020" growth plan.
In October, six workers were arrested after staff ripped off executives' shirts in an angry protest over 2,900 planned redundancies.
That figure was later revised down to 1,600 voluntary departures by the end of 2017, union officials said.
Air France-KLM pays 30% of overall revenue in wages, compared with 24% for Lufthansa and about 12% for a budget airline such as Ryanair.
Air France-KLM returned to profit in 2015 for the first time in four years, helped by lower fuel costs and higher passenger numbers.