Gulf state is aiming a significant increase the size of its air force, is looking to buy 72 jets.
French conglomerates Alstom and Vinci signed a €2bn ($2.72bn) deal with Qatar on Monday to build a tram system in the future Lusail City, while the two countries also discussed a possible defence contract.
The deal, which will see the light rail system starting to operate in 2018-20, was signed in front of journalists during a visit to Paris by Qatar's emir, Sheikh Tamim bin Hamad Al Thani.
One of the Gulf's largest real estate developments, Lusail City is expected to house up to 200,000 people and contain commercial districts including the $275m Marina Mall project, 22 hotels, four islands and two golf courses.
The estimated $45bn development will also feature the 80,000-seat Lusail Stadium, where the championship match of the 2022 World Cup soccer tournament will be played.
Qatar has been under fire for its treatment of migrant workers, many of whom are reported to have died on the country's infrastructure projects, but has announced stricter measures for contractors involved in building work for the 2022 tournament.
Asked whether France had raised the issue of worker conditions during the emir's visit, a French official said, "We talk about everything with Qatar. There are no forbidden topics."
Leaders of the two countries also discussed the possible sale of French Rafale fighter jets, built by Dassault Aviation, to Qatar but there was no immediate conclusion.
"They discussed it. Negotiations are continuing," a source close to French President Francois Hollande said following a meeting held during the emir's first official visit to France.
Qatar is planning a significant increase in the size of its air force as the energy-rich Gulf state forges a wider international role after taking part in the 2011 Libya conflict.
Its air force operates a squadron of 12 Dassault Mirage-2000 jets, but is now looking to buy 72 jets in two equal tranches.
"Qatar has always chosen French technology for its armed forces," Hollande said in a speech toasting the visiting Qatari head of state before an official dinner.
The emir made no reference to the Rafale during his remarks, delivered in French.
France is anxious to secure its first export buyer for the Rafale as it also tries to close a long-awaited $15bn deal with India for a purchase of 126 of the multi-role jets.
In Qatar, Dassault Aviation is competing with the Eurofighter Typhoon - offered by a European consortium of Airbus Group, BAE Systems and Finmeccanica - and the F-15 fighter built by US planemaker Boeing.
"Traditionally, Qatar is a French stronghold in arms exports but they have been buying from elsewhere," said Douglas Barrie, senior fellow at the International Institute for Strategic Studies, noting speculation that Qatar might split the order and go for a mixed fleet despite incurring extra training costs.
"I would be surprised if the French walk away from this empty-handed. Is it beyond the bounds of possibility that someone else gets all 72 aircraft? No, but unlikely," he said.
Qatar is among a number of Gulf states looking to renew air power but also seen as playing a waiting game with Washington for the newer Lockheed Martin F-35.
The United States has not so far decided whether to offer its latest radar-evading combat jet to the Gulf, but arms sales experts say it could become available to the region about five years after Israel receives its first F-35 fighter jets in 2016.
US policy guidelines call for Israel to maintain a competitive military edge.
"The key question is whether the Americans will release the F-35 and if so when," Barrie said.
That, he said, would influence whether Qatar feels it can buy something in the interim and then make the case in Washington to release the F-35 into the region. Even then, competition for any interim deals is expected to be fierce.