Germany first began invading France on May 13, 1940; it fully invaded France on June 12 and captured Paris on June 13 of the same year. The German army was able to achieve this as it advanced into France via Belgium, which made it easier to bypass the country's fortifications.
To protect the country from the German army, France's president introduced the Maginot Line, which was an area of fortifications. Hitler was aware that the Allied forces expected them to advance via this line, so he allowed General Erich von Manstein to advance through the Ardennes, which was hillier and therefore easy to remain concealed in. This involved moving through Belgium, which was neutral at the time.
Hitler's forces first came close to France on May 13, 1940, leading to a battle between the German army, the Allied aircraft and French soldiers on the ground. On June 12, they managed to break through the Somme and defeated the Maginot line, allowing them to advance into Paris on June 13. Between their initial invasion and the Nazis' arrival in Paris, France evacuated many of its citizens to the countryside. By June 22, France was forced to sign an armistice with Germany. To mark the moment, Hitler insisted that they do so in the same train carriage used to make Germany sign an armistice during WWI.