Did fairs in medieval Europe implicitly encourage the wider use of money? It seems that local markets allowed simple bartering, but big fairs were more likely to use money for purchases because the fair was temporary and required debts to be settled quickly. So did these fairs (such as the Champagne fairs in France) lead to more use of government-minted money?
Up to a certain point, yes. But that is true for the increase in trade in general during the period of the 11th to the 13th century. An increase in trade stimulates monetary circulation.
However, this is not to say that the Champagne (and other) fairs were the driving force behind the increase in mint. One major reason was the discovery and exploitation of major silver mines in Eastern Europe.
But these fairs did certainly stimulate trade and play an important part in the economic development of this period. The fact that large fairs such as those of Champagne also had a financial market stimulated this even further. They used an early version of a letter of exchange, which could be transferred to different traders and different people as a means of transferring debts and money without having to transfer actual silver. This also means that what you said, "because these fairs only lasted a short time they would have to pay back fast", is not true.
But yes they did play a very important part in the economic development and trade of the period and so also the increase of monetary circulation and mint.