How were Kurds involved (or not) in the invasion of Normandy?

Question

In defending his decision to withdraw from northern Syria and cease supporting Kurdish fighters in the face of the 2019 Turkish invasion, Donald Trump said:

[The Kurds] didn’t help us in the second world war, they didn’t help us with Normandy as an example ...

What exactly is Trump talking about? In what way were Kurds involved, or not involved, in the invasion of Normandy? Was there a sizable Kurdish population in France, or a Kurdish contingent of the Allied Powers which refused to support the operation, or something else?

Answer 1

The Kurds had very little involvement in WWII and no capacity to take action as a group. At the time, just about all of them lived in the Kurdish areas of Turkey, Iran and Iraq. They had no self-determination, and those states acted as follows:

• Turkey was neutral throughout WWII.
• Iran was invaded and occupied jointly by the USSR and the British Empire in late summer 1941, to create a route for supplies to be sent to the USSR from India, and to secure control of the Iranian oil fields. The occupying powers withdrew after the end of the war, although the Soviets did not want to at first.
• Iraq was under British influence. There was a coup by Iraqis sympathetic to Germany in spring 1941 and an attempt to expel British forces, but it failed. The British recruited local troops, about 25% of whom were Kurds, but they were under British control. As per the link:

By 1942, the Iraq Levies consisted of a Headquarters, a Depot, Specialist Assyrian companies, 40 service companies and the 1st Parachute Company, which consisted of 75% Assyrian and 25% Kurd. The new Iraq Levies Disciplinary Code was based largely on the Indian Army Act.

By 1943 the Iraq Levies strength stood at 166 British officers controlling 44 companies; 22 Assyrian, five Mixed Assyrian/Yizidi, ten Kurdish, four Marsh Arabs, and three Baluchi. Eleven Assyrian companies served in Palestine and another four served in Cyprus. The Parachute Company was attached to the Royal Marine Commando and were active in Albania, Italy and Greece. In 1943/1944 the Iraq Levies were renamed the Royal Air Force Levies.

So a platoon or so of Kurds, in the Parachute Company, served in Albania, Italy and Greece with the Royal Marine Commandos, but they weren't at Normandy. There is no sign of any Iraqi units in the order of battle for Gold, Juno or Sword beaches.

The Kurds, as a people or a political group, did not have an important role in WWII, and there was no significant Kurdish diaspora to influence events elsewhere.

Addendum: More information about the Iraq Levies here and here.

Answer 2

Just some additional information, from an Oct. 10 NYT Article
_{(apologies if there's a paywall)}

... Did Kurds fight in World War II?

It is unclear whether any Kurds were at the Normandy landings, but there is evidence that some of them fought on the side of the Allied forces during World War II.

Some background: The Kurds, despite being the fourth-largest ethnic group in the Middle East, are a stateless and often marginalized people whose homeland stretches across Turkey, Syria, Iran, Iraq and Armenia. After World War I, the Allies’ negotiations with representatives of the defeated Ottoman Empire initially involved provisions for an autonomous Kurdistan. But that was abandoned by the ratification of the Treaty of Lausanne in 1923. Multiple attempts at greater autonomy or nationhood since then have been suppressed or quashed.

Some of the Kurds who had been pushed out of the Ottoman Empire and Turkey landed in the Soviet Union, said Mutlu Civiroglu, a Kurdish affairs analyst in Washington. So when World War II began, many fought with the Soviets on the side of the Allies. But they were difficult to track because they did not fight under a Kurdish flag.

“They didn’t have a country,” Mr. Civiroglu said. “They didn’t have a navy. They didn’t have anything on their own. But individually, many people came forward.”

Evidence of this has survived in folk songs and books that pay tributeto Kurds who fought in World War II, Mr. Civiroglu said. He also noted that Samand Aliyevich Siabandov — a member of the Yazidis, a Kurdish-speaking religious minority — was a well-known Soviet fighter who was lauded in the English-language Russian newspaper Moscow News in 1946.