I'll try my best to answer this question, but sadly I can only speak fro French resistance due to lack of time to type up anything about Soviet resistance.

Surprising the Allies

As with Operation Barbarossa, comparable surprise was achieved by the German plan of attack. This was partially helped by the fact of Hitler's lack of military knowledge. He wanted to attack France immediately after Poland, even though those in the German Chain of Command knew that Germany was not at all ready for war against a more modernised and capable army such as the French army and the British Expeditionary Force.

The German army was never as motorised as it is portrayed in the media, and those divisions that relied less on horses and were partially motorised had a huge lack of functioning vehicles, even more so after Fall Weiss, the invasion of Poland. The Army simply needed more time to obtain and produce the equipment needed for the Wehrmacht. Eric Brown, a British citizen in Bavaria at the time of the declaration of war, war picked up by the SS and taken to the Swiss border after 3 days. They took all his belongings, but returned his car. When asked why, the SS men replied that they had no spares so the car was worthless to them.

Also, the invasion of Poland happened in September, which meant that winter was coming on, which is never a good time to attack; Hitler wanted to attack immediately, while the generals wanted to wait until spring.

Hitler insisted that OKH produce a plan for the invasion of France through the Low Countries, and so General Halder and his team were put to the job. Halder, at that time connected to the resistance and assassination plot against the Fuhrer, believed that to attack France at this time would be madness, so he aimed to make the plan so self-evidently bad that even Hitler himself would have to postpone the invasion until a better one could be found.

However, the ultimate deception plan came to the fore when on the 10th of January a German aircraft was forced to land in Belgium. This aircraft contained plans for the German attack, and they were captured before they could be burned. In the following weeks, German reconnaissance watched allied troop movements all along the front, and it showed that the Allies had been expecting an attack almost exactly the same as Halder's plans detailed. Another event that helped Halder was the French reaction to German movements along the front; it took the French around two weeks to notice a change in German troop placement and adapt to it.

Halder took this as an opportunity to test out a plan that a German Corps commander, von Manstein, had come up with. It was the plan that would become Fall Gelb, Case Yellow. Armeegruppe B would smash through into Holland and Belgium, while Armeegruppe A (with most of the Panzer forces) would attack through the Ardennes forest in Southern Belgium and Luxembourg, with the aim of crossing the Meuse. Based on the previous reaction times of the French, theoretically German forces would be able to make it through the rough terrain of the Ardennes before the French realised what was going on. This would mean that most of the British and French forces would rush into Belgium and the Netherlands to counter Armeegruppe B's feign attack, while Armeegruppe A coming through the Ardennes would be able to push North-West from the Meuse, surrounding and creating a Kessel - a cauldron (often referred to as a pocket) - around the majority of the British and French forces. It was a huge gamble, but Halder knew Hitler would jump at the suggestion of such a daring plan, and so this was chosen as the main plan for the assault on the West, creating the surprise the Wehrmacht needed.

The Resistance by the Allies

It is well known that the German plan worked, and a huge amount of allied forces were surrounded, culminating in Operation Dynamo, the famous evacuation of British and French forces from the beaches of Dunkirk. However, the French did put up some resistance. For example General de Gaulle performed multiple actions against German Panzers.

The first occurred when de Gaulle attacked and nearly overran the headquarters of the 1st Panzer Division with the 4th Armoured division, although the swift German reaction with Panzers and Luftwaffe support badly battered de Gaulle's forced, which lacked anti-aircraft guns and fighter cover. A lack of fighter cover also foiled another attack by de Gaulle with 150 tanks a few days later.

However, much of the French army's resistance was token or futile. Panzers often simply drove past French troops on the road and shouted at the them to throw down their weapons and march Eastwards, the French often obliging.

In his book 'The Second World War', Antony Beevor describes the state of General Billotte's First Army Group HQ. 'Billotte's headquarters were in a state of psychological collapse, with many officers in tears. Gort's [Commander of the BEF] chief of staff was so horrified by what he had heard from the British liason officer that he rang the war office in London to warn them that the BEF might have to be evacuated at some point.'

French morale was often appalling; before the invasion, French soldiers were shocked when asked why they were not shooting at German patrols. 'Then they would shook back!' they exclaimed.

By the 15th of June, the armistice was signed and France had surrendered. I'm sorry I can't give more detail because I've got to go out but I hope this helped. I will attempt to add more detail and maybe some Soviet context when I get home in around 6 goes from the time of posting.

Sources:

The Second World War - Antony Beevor

The War in the West Volume 1 - James Holland

The World at War - Richard Holmes [Transcripts of interviews from the Tv series)