From what I remember my history teacher said Germany invaded France in a week

Although I can't comment on exactly HOW LONG it took the Germans to enter France, the initial fighting up until the end of the Dunkirk Evacuation, what the Wehrmacht termed Fall Gelb or Case Yellow, was confined to Netherlands, Belgium, and France north of the Somme and Meuse rivers. I get the feeling they were implying that defeat took a week, which it did not. The campaign in France and the Low Countries , covering Cases Yellow and Red, lasted 6-7 weeks, and was the scene of intense fighting.

From what I remember he also said typically a country declares war before engaging, Germany didn't do it so France was surprised

Considering that the Netherlands and Belgium were invaded first, by Army Group B, and also taking into account German airstrikes and the Bf 108 incident in January 1940, which saw a German officer crash in Belgium with plans for the invasion in the West, the surprise was not so overwhelming.

France was also defending with horses against German tanks

France and Britain together had more tanks than Germany, and were far more motorized and mechanized than the German Army which, outside of the Panzer and motorized infantry divisions, was entirely dependant on horse transport. The French also made use of horse transport, and both armies fielded cavalry in the campaigns of summer, 1940.

But the Germans bypassed it somehow but how?

The French had set about constructing the Maginot Line along their border with Germany and Luxembourg in the late 20s. I have given answers about it [here] (https://www.reddit.com/r/AskHistorians/comments/2onrnk/after_world_war_i_france_was_the_most_powerful/cmoxmga?context=3), [here] (https://www.reddit.com/r/AskHistorians/comments/2zijiq/if_the_french_had_not_built_the_maginot_line/), and [here] (https://www.reddit.com/r/AskHistorians/comments/3412u1/in_wwii_why_did_the_siegfried_line_work_when_the/). Essentially, the whole point of the Maginot Line was to FORCE the Germans to bypass it, thus ensuring that any future conflict would pit Germany against France, Belgium and Britain, and on terms that favoured the latter three. The Germans did bypass it, exactly as expected. What the French did not anticipate was that the Germans would send almost all over their motorized/mechanized forces through the Ardennes, a potential death trap, and that in the event of such a happening: A) the Luftwaffe would have air superiority and B) the French would have no strategic reserve to speak of. Combine this with the lethargy of the French Air Force and Army High Command, and the Battle of France becomes less a case of 'Germany fighting the next war v France and Britain fighting the last war' and more 'Germany took a massive risk, that paid off due to key mistakes by the allies'. As I note, however, in those answers I gave, the Maginot Line essentially did it's job, and proved a tough nut to crack in 1940 and 1944.

Hey there, you may be interested in two previous questions on the Fall of France I've answered with help from /u/DuxBelisarius :

What was the cause of French Failure in WW2? and;

How come Germany was so much stronger than France?

Feel free to ask follow-on questions.

Since you're NOT already conversant with the German invasion of France (1940), I will keep my response at an extremely exoteric level. If you have any questions about more details on any specific part of the very light narrative below, fee free to ask.

France, on its eastern side, shares its border (from north to south) with the Low Countries, Germany, Switzerland and Italy. Check out this map of Western Europe in 1940. The Low Countries refers to Netherlands, Belgium and Luxembourg.

After the First World War, France built a massively fortified line of defence – the Maginot Line – along its border with Germany, to act as a deterrent and as an impervious obstacle to any future German aggression. The Maginot Line was no joke and was really considered to be impregnable by most analysts of the period.

The Maginot Line featured a massive concentration of powerful artillery pieces encased in concrete turrets, an assortment of anti-tank obstacles, and it was up to 20 km deep. It took 9 years to construct and was one of the most fortified places on earth in 1940. It was built in such a way that those manning it can repel an army twice or thrice larger in number; that way, France can deploy the bulk of their army along their border with the Low Countries in the event of war with Germany.

So when war broke out between France and Germany in September 1939, France mobilized their army and moved the bulk of them to their border with the Low Countries. Britain also sent a lot of troops and war material to aid France. Germany at this time was busy fighting Poland, and later moved on to invade and conquer Norway and Denmark; all the while France organized their army and prepared their defences.

There are several present-day historians who argue that France could have beaten Germany if they attacked while Germany was still busy fighting all those countries. Well, that is debatable.

Finally, when Germany was done dealing with its eastern and northern neighbours, it turned its attention on France. The Germans decided to launch their main attack through the Ardennes Forest that covered the northern part of Luxembourg and the southern tip of Belgium. The Ardennes Forest, with its numerous streams, rolling hills and ridges, was a tough terrain for both infantry and tanks. The French believed that Germany will surely attack through northern and central Belgium because an attack through the Ardennes Forest or through the Maginot Line will require too much effort or prove too risky, so they placed the bulk of their armies along their border with northern and central Belgium.

The German General, Erich von Manstein, developed the German plan for the invasion. In this plan the Germans decided to attack through the Ardennes Forest (no matter how troublesome the terrain may prove), and then rush as fast as possible, bypassing and ignoring any non-mobile French forces along the way, and reach the English Channel asap. The result would be that the bulk of the French army will be cut off from their sources of supply and therefore effectively encircled with their backs to the English Channel.

This encirclement will be possible because the other group of German forces sweeping in from northern and central Belgium will block the eastern front line of the French forces, while the German forces that broke through the Ardennes Forest will block their southern and western front line; the English Channel takes care of their northern side. Once the French army (and the British forces that came to aid them) have been encircled, the Germans can then focus on destroying them in to to. After they've wiped out the best that France and Britain had deployed, the Germans can then move south and attack the Maginot Line from both front and behind.

The Germans invaded on 10 May 1940, and everything (for the most part) went according to plan. On 20 May they reached the English Channel, and France was doomed. Almost all the British troops in France, along with a huge portion of the French army, were trapped in the huge encirclement; and their back was to the English Channel. That's probably where you history teacher got the idea that Germany "invaded France in a week".

From 27 May to 4 June, the British launched Operation Dynamo (a.k.a Miracle of Dunkirk) and evacuated everyone that they could that were trapped in the encirclement. This was a significant success for Britain, because the soldiers lived to fight another day. With the business of the encirclement finished, the Germans then turned their attention to the rest of France. The rest of the invasion is history. On 22 June, the French government signed the surrender of France (the surrender took effect on 25 June).