There is not a whole lot in common with most historical Romanian script unless it is assumed to have been inscribed during the transition from church Latin (ending around 1190's) to subsequent Cyrillic (2nd half of 13th century.)
During this transition period some example script appears similar to what is inscribed on the sword. The "X's" at that time were pronounced with the abundant sound of the regions' speech now best represented in modern alphabet with "ck" or "ks." Some surviving 13th century coins (Wallachian I think) actually exhibit 2 "X's" interspersed within single words, as well a similar style font and anchor ended crosses with stars in the corners (reminding me of the symbols bordering the text of the river find sword.)

During the late 12th to early 13th century time frame, there were numerous Germanic and a couple of French and Flemish knights that immigrated into Romania to safeguard it against neighboring foreigners. Even the Teutonic order moved in to border regions for a little over a decade before expulsion in 1226. At the same time, there was crusade contact and pilgrimages that passed right through the territory. Magistrates and land holders (gereb) in Saxon held regions were semi-nobles that eventually did become something of a nobility by 14th century.

I admit it is a very far fetched stretch, but if I am going to criticize the museum's explanation for "runes", I figure I should at least try to offer a semi-plausible alternative explanation. Anyhow, I don't buy the official museum explanation for the inscription.