What tactics did Germany use in France?

Answer 1

This would be the "Battle of France" in 1940. In short: The German armies used rapid movement based warfare with aircraft as close support to replace the slow moving artillery units and won an old fashioned war of manoeuvre against a static enemy.

In long: They concentrated their armoured units and fast moving support infantry into "spear heads" which broke through the French and British lines allowing units to move rapidly (dangerously far infact) into the rear areas of the allies, capturing supply dumps, overrunning airfields, destroying communications networks.

The continuous speed of the German advance continued to catch units before they could form new lines, the concentrated force of the spear head overwhelmed resistance - for instance Allied armour was spread thin along their units, German armour concentrated in the thrusts - and forced the retreat of the units to either side.

The Allied armies couldn't react fast enough to close the gaps and so retreated to try and reform their line, command and control broke down, the roads were crowed with routed troops and civilian refugees making the job of reforming units even harder.

The best equipped French units had advanced into Belgium expecting a rerun of the first world war and were out flanked by the German thrust through the heavily wooded Ardennes region. This left a French army group and the British Expeditionary Force pinned against the channel coast while the majority of the French army, now missing it's best armoured units, pushed south towards Paris the Battle of France was all but won. (Or lost!)