It is most important not to confuse a free trade policy with a Customs Union policy. The main point about a Customs Union is the wish to impose tariffs and barriers against the rest of the world that are legal under WTO rules, knowing that the WTO would prefer the members of the Customs Union to lower tariffs and barriers for all.
Much of the design of the EU Customs Union was to protect French and German industry from better value or smarter competition from elsewhere in the world, and to protect the exploitation of market niches that they had done well so far. One of the features I most dislike about the EU Customs Union is its aggressive stance towards emerging economies which rely heavily on agricultural production, as the EU Customs Union takes full advantage of the WTO permission to have strong restrictions on agriculture.
Germany, for example, has a profitable and large industry processing raw coffee. This is made possible by imposing tariffs on processed coffee from outside the EU whilst allowing import of raw coffee tariff free. It means the coffee producers find it more difficult to capture the extra added value and create the extra jobs that are needed to turn an agricultural product into coffee to drink in supermarket packaging.
Once out of the EU Customs Union the UK could unilaterally cut all tariffs on products we do not grow for ourselves, or could offer to do so in return for some free trade response from those who would benefit. Inside the EU Customs Union we cannot do this, as the others do not agree with such a strategy. Trade is often better than aid in promoting economic development and greater prosperity amongst emerging economies. The Uk will be able to have a better policy for this once we are free to negotiate our own trade system.