Dassault, a French aerospace company, is one of three aircraft makers who are under consideration by Lula for a $2bn contract to build 36 fighter aircraft for the Brzailian air force.
The Rafale fighter jet is considered to be Lula's preferred choice over the US F/A-18 Super Hornet and the Gripen NG, built by Saab, a Swedish company.
The Brazilian president said before Sarkozy's visit that Dassault’s offer had an "exceptional comparative advantage" because Paris has agreed to share all military technology with Brazil as part of the deal.
Talks with France over the Rafale aircraft are at "a very advanced stage and I think that we will reach a good understanding with France," Lula said in a radio interview.
Brazil last December agreed to buy five submarines and 50 military transport helicopters from France, in a deal worth about $10bn.
Sarkozy and Lula were set to sign the final confirmation of those two major purchases on Monday.
Brazil is modernising its military in an attempt to protect its natural resources in the Amazon and new offshore oil fields.
Lula has said that Brazil's overhaul of the military is part of a strategy aimed at establishing the country as one of the world’s 10 major powers.