I’m going to stick with 15th-century England, in which the answer is: probably nothing.

Long story, but it’s going to get relevant: in 1483, Edward IV died. His eldest son was 12, so Edward’s brother Richard became Lord Protector, as specified by Edward’s will. While Richard was making preparations for his nephew’s coronation, Robert Stillington, Bishop of Bath and Wells and Edward’s Lord Chancellor, came forward to say that, before Edward married the boy’s mother Elizabeth Woodville, Stillington had precontracted (betrothed) him to another woman - Lady Eleanor Butler. This meant that the marriage to Elizabeth Woodville was invalid, the boy was illegitimate, and Richard was king.

There’s argument about whether this claim was true (unclear), and about whether Richard put the priest up to saying it (unlikely, IMO, given his actions in the immediate aftermath), but neither of those issues is relevant to your question. The point is: at that time and place, it’s clear that betrothal was taken very seriously, to the point where it was basically a semi-formalised marriage. It was serious enough to invalidate a later marriage to another person, and make the children of that marriage illegitimate. Richard’s opponents argued that the precontract story was bollocks, but they don’t seem to have argued that Edward’s children would be legitimate even if the precontract had taken place. Titulus Regius, the act in which Parliament asked Richard to take over as king, uses the terms ‘married’ and ‘precontracted’ as if they’re to all intents and purposes interchangeable:

The seid King Edward was and stode maryed and trouth plight to oone Dame Elianor Butteler, Doughter of the old Earl of Shrewesbury, with whom the same King Edward had made a precontracte of Matrimonie, longe tyyme bifore he made the said pretensed Mariage with the said Elizabeth Grey, in maner and fourme abovesaid. Which premisses being true, as in veray trouth they been true, it appearreth and foloweth evidently, that the said King Edward duryng his lif, and the seid Elizabeth, lived together sinfully and damnably in adultery…

There’s also the contemporary French chronicler Philippe de Commines’s account of the episode. De Commines says that Stillington said he precontracted Edward to ‘a beautiful young lady’ because Edward wanted to have sex with her and that was the only way she would consent:

The bishop discovered to the Duke of Gloucester that his brother king Edward had been formerly in love with a beautiful young lady and had promised her marriage upon condition that he might lie with her; the lady consented, and, as the bishop affirmed, he married them when nobody was present but they two and himself.

So not only did a young noblewoman consider betrothal to be close enough to marriage, both in moral terms and in terms of social consequences, to make sex acceptable - a bishop felt the same way. (Edit: Even if the precontract story was in fact bollocks, a bishop considered it plausible that both he and the young noblewoman would see sex as acceptable under those circumstances - and de Commines doesn’t seem to consider this odd or surprising either.)

In that time and place, anyway, you and your groom-to-be are good to go.