His remarks came ahead of an agreement normalising relations between Turkey and Armenia to be signed in Switzerland on Saturday.
With regard to Turkey's EU ambitions, Sarkozy reaffirmed "in a very frank manner the French position" while Gul "recalled Turkey's views in just a frank and friendly manner," the Elysee said.
"All issues were raised in a good spirit of co-operation and mutual respect," the office said.
The Turkish president gave no media statement after the hour-long meeting, but the Elysee said that the talks had "concluded with a resolve to work more closely together, in all fields both diplomatic and economic".
The French president suggested that Paris and Ankara could work on civilian nuclear energy, according to the Elysee, saying that Gul had welcomed the idea as "very encouraging".
Gul also told Sarkozy that Turkey would welcome GDF Suez, a French-based energy company, back to the EU-led Nabucco pipeline project linking Central Asia to Europe, after the company was sidelined from the six-nation consortium early last year.
Officials suggested at the time that Ankara vetoed France's bid in reprisal for the French parliament's decision to recognise as genocide the killings of 1.5 million Armenians, according to the Armenian government, during and after the first world war.
Gul assured Sarkozy that "French companies are welcome in the project," the Elysee said.
Earlier Gul and Sarkozy jointly opened a major Paris exhibition on Istanbul, the flagship event in a season of events celebrating Turkish history and culture in France.
The Turkish leader also met Francois Fillon, the French prime minister, during his Paris stay, with both calling for France and Turkey to step up reciprocal business investments.
Turkey began membership negotiations for the EU in 2005, but has so far opened talks in only 11 of the 35 policy areas that candidates must complete, while France, Germany and other EU members have sought to slow or halt the process.
Sarkozy says Turkey, of which only a small portion is geographically in Europe, should settle for a partnership agreement.