Spitfires weren't deployed to France in 1939-40. RAF Fighter Command resisted deploying Spitfires in France, preferring to save them for the defense of Britain; Spitfires were used to cover the evacuation at Dunkirk, but they were based in England. In the novel Hornet Squadron flew Hawker Hurricanes. Hurricanes were more numerous in 1939-40 because they were easier to build and cheaper. Because of their greater numbers it is often said that Hurricanes were the mainstay fighter during the Battle of Britain, not the Spitfire; in reality the two types worked in concert, with Hurricanes deployed to attack the bombers while Spitfires were used counter the Luftwaffe's escorting fighters.
The Spitfires shown are all armed with cannons. In 1939 they were armed only with machine guns. This is inevitable because few early model Spitfires would be in flying condition to use, even in 1988.
RAF Squadrons then as now are numbered without a type designation, such as bomber or fighter. Hornet Squadron is stand in for RAF fighter squadrons in general.