What kind of ship?
Typical medieval ships were not particularly known for their sailing prowess. The Hulk is the most likely sailing vessel one might expect to see sailing a river, but these were likely towed or rowed upriver with the expectation of sailing downriver. The hulk's successor, the Caravel, could definitely have managed to sail upriver given almost any wind conditions. This ship type, however, did not appear until the 15th century. The Portuguese navy of the time most likely utilized rowed warships with supplementary sails. In general, I would assume rowing would be the most prevalent method of upriver propulsion.
I should mention that the Caravel was invented in Portugal in the 1400s and its invention led directly to the Age of Discovery. Depending on how hand-wavey you are willing to be with your history, it might be plausible that your heroes managed to get their hands on an early prototype of this kind of vessel, allowing them to actually sail upriver rather than row.
That being said, there is an outside chance that a pair of people could manage to sail a small vessel by themselves, but they would need to be skilled sailors to manage the necessary tacking in uncooperative winds. A skilled crew would be needed for a ship of any appreciable size, and if the ship needed to be rowed at any point, they would almost certainly need a crew to do this. It is very unlikely your heroes could manage this journey alone unless they were aboard a very small boat of some sort.
What Season is it?
It has been unreasonably difficult for me to find meteorological data about Portugal and the prevailing winds, but from what I can tell there should always be at least some wind. The winds are more powerful during the summer months and weaker in the winter, but they rarely seem to die completely. Sailing in the summer will probably be the best choice for your heroes, since the winds are steady and predictable. It seems they typically blow West in the afternoon and East in the morning, with bouts of North/South in between.* A skilled sailor could utilize practically all wind directions if they are using a ship like a Caravel. Travelling farther inland may prove troublesome, however, since the winds will likely become less predictable no matter the season. Regardless, your heroes will need to acquire a sound understanding of the weather of the region in order to handle the trip up the river, and will need to know how to handle any winds they encounter.
What is their final destination?
This question may seem out of place, but bear with me. Heading upriver, The Douro travels inland from Porto, hits the border with Spain (even in the 14th century this was the border between Spain and Portugal) and follows the border for some miles until hooking into East into Spain and eventually climbing up into the mountains to find its headwaters. This is important because along the international border the river becomes narrower, and this is the location of the river's steepest point of descent, altogether proving to be the most challenging location to sail upriver. If the heroes simply need to enter Spain, they could disembark at the first sign of the border and avoid this area, but if their journey needs to take them into the heart of Spain they'll need to go through this region and manage the more difficult river conditions. At no point do I suspect the river is too narrow or too steep to manage by a skilled crew but this would prove to be yet another challenge to your heroes.
Or they could take a horse.
*My knowledge of meteorology is rudimentary at best. I ask anyone to check my statement and correct me if I am mistaken.