Chirac told a news conference on Monday: "Saudi Arabia is actively pursuing a detailed study of different solutions" proposed to Riyadh in terms of co-operation in defence and security.
"All this is taking place in an excellent climate."
At stake is the sale of French Rafale fighters and a border monitoring system to Saudi Arabia, which a French presidential spokesman had cautioned would not be finalised during the trip, Chirac's fourth to the Gulf country.
Dassault Aviation, a French aerospace group, confirmed last April that talks had taken place on the purchase of the Rafale.
The French daily Les Echos said at the time the discussions focused on the purchase of 48 fighters with an option for 48 more in a deal valued at $7.2 billion (€6 billion).
The fourth-generation Rafale, a multi-role combat jet which can carry out interception and reconnaissance missions as well as nuclear strikes, has yet to find an export market.
The other potential deal involves the Miksa electronic border monitoring system, under which electronic defence manufacturer Thales would supply 225 radars to Saudi Arabia over a period of 12 years for $8.4 billion (€7 billion).
The sale of the Miksa - the acronym for Ministry of Interior Kingdom of Saudi Arabia - would also include a telecommunications network, reconnaissance aircraft and about 20 helicopters.
Chirac, whose visit came two months after it was announced that Saudi Arabia would buy Typhoon Eurofighter jets from Britain, said he was pleased by the contacts established between more than a dozen French business people and industrialists accompanying him and Saudi counterparts.
Thierry Demarest, the chairman of Total, meanwhile said he hoped to conclude a deal to build a five-billion-dollar oil refinery in Saudi Arabia's oil-rich Eastern Province within months.
"We have always condemned what some call the clash of civilizations, and which I call the clash of ignorances"
He said: "We still need some time ... a few weeks to a few months if we continue to progress as we have done so far."
There remain "a number of problems to be resolved," Demarest said.
The refinery, with a capacity of 400,000 barrels per day (bpd), would be built in Jubail on the Gulf coast. Although he did not give a specific figure, Demarest said such ventures usually do not cost less than $5 billion.
Tolerance and respect
Chirac, who on Sunday became the first foreign leader to address the Saudi appointed Shura (consultative) Council, took advantage of his presence in the kingdom, home to Islam's holiest sites, to advocate tolerance and mutual respect at a time when Muslims across the world have been infuriated by the publication of blasphemous cartoons depicting Prophet Muhammad.
He said: "We have always condemned what some call the clash of civilisations, and which I call the clash of ignorances."
On regional issues, Chirac said he was "disappointed" by Iran's attitude in the crisis over its nuclear programme, while stressing that the international community would not decrease its effort to convince Tehran to "respect its commitments" to suspend enrichment activities.
His remarks came as the International Atomic Energy Agency began a meeting in Vienna that could lead to punitive UN Security Council action against Iran.
Chirac also said he "respected" Saudi Arabia's decision to oppose a reduction of Opec's output so as not to push oil prices further up when the cartel meets in Vienna on Wednesday.