Im sorry, what?A seax and later on the (lange/große) Messer was a long knife, i.e. a single edged weapon, a sword (spatha) is always double edged and was only used by knights (and legally reserved for them)
There are plenty of double edged knives throughout history, and plenty of single edged swords too, unless for some strange reason you think sabers, cutlases, katanas, etc, aren't swords.
And swords were never illegal for commoners to own. In many cases they're legally required, and in some cases you may be restricted in length or where&when you can carry them, but never could they not own them