Well I wouldn't say anyone was to blame. They were just more or less expecting a different kind of conflict. They were expecting a return to the static fighting of world war I. The plan was that when the German offensive started, the French and British would move into Belgium into a position that was more easily defensible. They thought this was the only invasion route the germans could take as they were unlikely to assault the maginot line directly. In fact the Germans were planning on doing just what the allies expecting when a small German plane got lost and crashed in Belgium with a copy of the invasion plan. German high command now had to come with something else. What they came up with was a daring plan to send the bulk of their army and panzers through the what was thought to be the unpassable ardennes forest. The allies had not expected this at all and the Germans were able to come out behind them and almost completely encircle them in Belgium. If it weren't for the fact that the German offensive was out running it's supply lines and was forced to slow down, the whole BEF probably would've been wiped out instead of rescued at Dunkirk.

So the answer to your question is that no one is really to blame. The British and French had planned for what they expected the Germans to do. Which was what the Germans had expected themselves to do. You could argue that an outdated understanding of what the role of tanks was in modern warfare was as a major misstep on the part of the French, but they did create three armor divisions (albeit very hastily) with little effect.