Does God allow common-law marriages?
Think about it for a moment. Let's say a country considers two people married for legal purposes if they live seven years together. Then what is this couple after living together for the first month? They aren't married; yet, they are having sex. Is that not fornication? Thus, the only way to achieve a common-law marriage is to continuously commit fornication for a period of time. The end does not justify sin. "And why not say, "Let us do evil that good may come"? --as we are slanderously reported and as some affirm that we say. Their condemnation is just" (Romans 3:8).
Marriage in the Bible is based on the covenant made between a man and a woman. "Yet she is your companion and your wife by covenant" (Malachi 2:14). A covenant involves vows, but it is not the same as a vow. There are several requirements for a covenant to exist. See: What are covenants? and Marriage Covenants. Where the covenant is made is not important. What important is that formal vows are exchanged in front of witnesses and before God with a record kept showing the existence of the covenant. Thus, private promises are insufficient for the purpose of a marriage covenant.