For a beginner, 'Mission to Paris' is a great start. It has a relatively straightforward plot compared to some of his other works. It's set in Paris during a time of great political unrest. The main character is an actor who gets caught up in some espionage activities. It's easy to follow and gives you a good feel for Furst's way of writing.
I think 'Kingdom of Shadows' would be a good starting point. It has all the elements that make Alan Furst's novels so great. There's mystery, historical backdrop, and well - developed characters. You'll be introduced to his world of spies and intrigue during a particular period in history. It's not too dense, so it's accessible for those new to his writing.
Definitely consider 'The Spies of Warsaw'. It offers a captivating look into the world of espionage in pre - World War II Europe. The story moves at a good pace and the characters are interesting. Furst's attention to detail in terms of the historical setting is on full display here. Reading this as your first Furst novel will give you an idea of what to expect from his other works.