By Jon Cronin
BBC News business reporter
As Jacques Chirac cuts a swathe on his tour of Saudi Arabia, there will be those among the French president's entourage hoping that his three-day charm offensive will lead to big orders for French business.
France still has high hopes that its defence firms will win Saudi deals
Not least, the bosses of two of France's leading defence companies, Thales and Dassault Aviation.
Saudi Arabia is set to spend billions of dollars updating its military hardware, from fighter jets to security equipment.
The oil-rich Middle East kingdom has traditionally sourced its arms from suppliers in the US and Britain.
The massive al-Yamamah arms deals between BAE Systems' predecessor British Aerospace and Saudi government in the 1980s was the biggest of its kind in British history.
But, as the political ties between Paris and Riyadh grow warmer, French defence companies believe they are close to muscling in on the action.
President Chirac has certainly played his part in improving their chances.
Jacques Chirac wants a bigger slice of Saudi defence spending
On Sunday, he became the first non-Arab leader to address Saudi Arabia's Shura, or consultative assembly, before heading into talks with King Abdullah.
Keen to show that France is serious about doing business in Saudi Arabia, the president's travelling companions include his economy, trade, defence and foreign ministers as well as the chief executives of some of France's biggest firms, including oil giant Total and electronics group Alcatel.
For a decade Thales has been battling to win a 7bn euros ($8.4bn; £4.8bn) deal to supply Saudi Arabia with border security equipment.
Meanwhile, Dassault has been lobbying hard for Riyadh and the Saudi air force to buy its Rafale fighter jets.
Despite the prior close involvement of President Chirac on behalf of Thales and Dassault, defence analysts had largely written off French hopes.
In December last year, Britain's Ministry of Defence announced that it had signed a memorandum of understanding with Saudi Arabia to supply its air force with dozens of Eurofighter jets in a deal rumoured to be worth £6bn.
The agreement appeared to secure Britain's continuing role as a major arms exporter to the Arab state, having supplied Saudi Arabia with Tornado jets during the late 1980s.
Until the French president's visit this weekend, Thales' hopes were also thought to be all but dead.
But emerging from talks with his Saudi counterparts, President Chirac signalled that the Saudi government was still considering buying French.
"We discussed (these deals) in an excellent climate, as is usual with Saudi Arabia," President Chirac told reporters. "Saudi Arabia is actively pursuing a detailed study on different options."
"France gives great importance to the ongoing study and to the decision the Saudis will take," he added.
Thales chief executive Denis Ranque also remains upbeat about his company's prospects.
"It is a question of timing, I am still confident. The prospective customer exists, the contract will exist, but it is taking more time than planned," he said.
As yet, no official word has come from the Saudi government on either Thales or Dassault.
But, as President Chirac continues to make friends in Riyadh, France's political and business elite believe that it is still too early to write-off French hopes.