For much of the Early Middle Ages clandestine marriages were regarded as entirely improper and unacceptable. The Byzantines went so far as to declare any marriage contracted without the blessing of a priest invalid. Legalists in Western Europe did not go as far, but they made their disapproval clear.
This disapproval did little or nothing to prevent people from marrying clandestinely, and in some places the practice was quite common.* It was only in the 12th century that the issue began to be discussed in much greater detail. The question of validity was a big one. It was all well and good to say that a marriage contracted clandestinely was valid, but then one had to be able to tell whether a marriage had actually been contracted. They were open to all sorts of confusion over intent (e.g. when one partner assumed they were married but the other didn’t, or when consent wasn’t freely given) and led to uncertainty about the legitimacy of the couple’s children.
Another serious problem for these writers was the fact that many people who entered into clandestine, informal marriages often dissolved them just as quietly and informally, which ran directly counter to the doctrine of the indissolubility of marriage (i.e. the idea that a marriage can only be ended by death) that the Church had been emphasizing for centuries.
For all that medieval legalists were clearly very concerned about clandestine marriage, they couldn’t really manage to reduce its frequency.** Some civil authorities imposed fines, but nothing terribly organized. By the 15th century marriage was considered a sacrament, but only if it was performed publically. In the end though, for all of the problems it caused clandestine marriage continued to be common, no matter what the Church had to say about it.
*The evidence of court cases shows us that even when families disapproved they generally tried to make the best of it rather than trying to separate the couple.
**Even the requirement by the Fourth Lateran Council (1215) that marriages be blessed by a priest only led to a thriving trade for priests willing to disregard pesky things like previous divorces.