To be more precise: in 1966, France left indeed the integrated military structure, but it did not left NATO itself which is also a political structure. The goal of de Gaulle was to have all French troups under only French command (and not US or UK who were leading nearly everything then in NATO) and to have all foreign military bases leave France, so that France regains its full sovereignty. De Gaulle was very critical of the US wars led at the time actually and he wanted to have Europe independent from both the USSR and the USA (and as he considered the UK as the pawn of the USA and not reliable in their commitment to Europe, he was opposed to them entering the EU). A fun fact was that it was also a incidentally a smart move economically, even if those US military bases closings were hurting the towns they were in: because of the Mansfield agreements around precisely 1966, Germany which still had US bases was giving more and more money as part of participating to the defense of Germany (2 billions $ in the year 1971 alone for example). This is quite like what president Trump tried to reinstate very recently by presenting a bill to Angela Merkel, but Germany now is not the same as West Germany in 1966.

You are comparing apples and oranges though. NATO is a purely military alliance. It has no control over the non-military affairs of member states, and little or no effect on the day-to-day lives of member states' citizens. The EU, on the other hand, acts very much like a central government for its members and exerts a lot of pressure on them to make them comply with its policies. That's why I compared it to empires.

What exactly are to "punishments" the EU is giving the UK that you are talking about?