Generally speaking the answer is no. Unlike items such as axes or bows - which in a rural situation can all be justified as tools, a swords purpose is to harm or kill others, and as such were restricted to those whos position would warrant them. Instead, peasants would typically carry a knife, such as a Long Knife, which can be seen in this drawing from 1497.

The following is from Close Rolls, Richard II: December 1393, Calendar of Close Rolls, Richard II: volume 5: 1392-1396, and can clearly show that in the London area at least the law regarding the carrying of a sword.

“To the mayor and sheriffs of London. Order to cause proclamation to be made, forbidding any man of whatsoever estate or condition to make unlawful assemblies in the city or suburbs of London, to go armed, girt with a sword or arrayed with unwonted harness, carry with him such arms, swords or harness, or do aught whereby the peace may be broken or the statutes concerning the bearing of arms contrary to the peace, or any of the people be disturbed or put in fear, under pain of losing his arms etc. and of imprisonment at the king's will, except lords, great men, knights and esquires of good estate, other men upon entering or leaving the city, and the king's officers and ministers appointed to keep the peace; and order after such proclamation to arrest all whom they shall find acting contrary to the same with the exceptions aforesaid, their followers, the arms, swords etc. found with them, and to keep them in custody in prison until further order, causing their arms etc. to be appraised and answer to be made to the king for them, and certifying in chancery from time to time the names of those arrested and the price and value of their arms etc. and so behaving that henceforward no more mischief be there done by their default; as it has now newly come to the king's ears that there are evildoers and breakers of the peace, some armed, some girt about the midst with swords, and some arrayed as aforesaid, who lurk in divers places within the city and suburbs and run to and fro committing batteries, mayhems, robberies, manslaughters etc., and hindering and disturbing the ministers and officers of the city from the exercise of their offices, in contempt of the king and breach of the peace, to the disturbance and terror of the people and contrary to the said statutes, which the king will not and ought not to endure.”