Turkey, which has NATO's second-largest army, has said the pact with nuclear-armed Pakistan and top oil exporter Saudi Arabia was open to expansion.
Norway becomes the latest country to receive France's nuclear protection, after Poland and Lithuania, which also share borders with Russia.
Saudi Arabia made a direct appeal to buy the jets earlier this year to Trump.
The senior Saudi official, who spoke on condition of anonymity, acknowledged the need to balance relations with Pakistan's rival, India, also a nuclear power.