As far I know they embarked ship Transylvania in Constanța and sailed to Alexandria in 1940. From there they traveled with the ship Compiegne to France. Many Czechs, Slovaks and Poles were on the run after Poland was defeated and some of them went to Russia and some to France. Heliodor Píka was instrumental in this endeavour.
Czechoslovak servicemen ended in Russian gulags with the charge of espionage as Stalin had Ribentropp-Molotow pact with Hitler. In France they fought against Wehrmacht but soon had to leave to England once France was defeated.
Even if my countrymen could have any reason to ignore France and UK war efforts due to Munich treason yet they still knew that Nazi Germany must be defeated and fought bravely for the just cause.
If interested, I could provide you with some details how Milan Píka described his story in an interview in 2018 shortly before he died few weeks ago.