In a statement, the Elysee Palace said Prince Charles expressed his gratitude to the royal family for the "deep mark of friendship shown by France during the Jubilee".
Macron gave the Queen a horse of the French Republican Guard to commemorate her birth anniversary, which he described to the emperor as the "golden thread" that tied France and Britain during his 70-year reign.
Elizabeth is known for her love of horses. Fabulo de Maucour, a seven-year-old gray gelding gifted by Macron, escorted the president down the Champs Elysees in Paris last month as part of an official ceremony.
Charles and Macron also discussed Ukraine in their phone conversation on Tuesday, Elysee said, noting that the two "agreed on the importance of maintaining the unity that has built between the allies since the start of the invasion."
They also discussed the consequences of the war in escalating global food insecurity as well as environmental issues.