Surely if a company in the UK wants to trade with one in France and Germany, they just get on with it, they dont have to go through the EU for permission.
They can get on with it, under WTO rules. But the whole point of trade agreements is to get better deals than that for the trading countries and their merchants.
For exactly the same sort of reasons other countries might seek agreements with the UK. Blocks of countries negotiate for all members. Members of no block have less "pull" and negotiate on their own. Until a trade agreement is in place the General Rules of Tariffs and Trade (GATT) often apply and these include high import barriers. Trade agreements normally take many years to conclude and many attempts fail altogether.
A basic trade deal should benefit both sides. The problem with the EU is they then start adding riders n such as fredom of movement. However I cnt see the USA agreeing to any freedom of movement (even Hillary) and trade still goes on between the US and the EU.
If the EU does not want a deal then fine, Tarrifs all round or no more UK sales for BMW, Audi, Mercedes,Renault,Citroen.