There really weren't any medieval wars in the conventional sense that lasted for decades or centuries on end. Medieval states - indeed, basically all states - were incapable of sustaining that level of effort for such a long period of time. Barring a decisive victory or the death of a leader, both sides would tend to become exhausted - short of men, money, and even food (remember: medieval warfare revolved around ravaging the countryside) - and negotiate a settlement or at least a truce. Whoever had done best in the fighting up to that time got the better end of the deal.

I'm more familiar with the Anarchy than I am with the Hundred Years War. The former was a brutal civil war fought to decide who would succeed the childless Henry I as king of England. Despite officially lasting from 1135-1153, open fighting only began in 1138, and it was mostly over by about 1147-48. Both sides exhausted themselves militarily, and after a few years of further skirmishing and negotiating, the war ended with a political compromise.

To use your example of the Hundred Years War, despite its name, it really consisted of several outbreaks of fighting interrupted by long stretches of peace, or at least not active campaigning. There were at least three major truces, and from 1340-41, 1360-1369, and 1389-1415, England and France were officially at peace. In addition to these, there were periods, sometimes lasting years, during which neither side actively campaigned.

In your situation, I would say that the most likely scenario would be that neither side has proven strong enough to defeat the other outright, and as a result, they have been at war off-and-on, with periods of peace

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