I think they'd normally stop somewhere in the British Isles. However, storms or trying to escape someone hostile and bigger could easily result in going somewhere unplanned.
Sailing south from Ireland along the coast of France means that you have the prevailing westerly winds from open sea towards the shore. Meaning that depending on the vagaries of weather, you may either be driven on a shore/reef, or have to take shelter at the nearest harbour, whose inhabitants may not like you.
Sailing from Western Fiords (Erik the Red's home, western tip of Iceland, 25 degrees West of Greenwich) or Cape Farewell (right next to another Erik the Red's home, southern tip of Greenland, 44 degrees West of Greenwich), a logical move might be to sail south across the open sea - no reefs, no enemies, no matter if you get blown a bit off course - until you reach the latitude of your destination, and then run downwind before the prevailing westerlies to make a landfall near the destination you know as friendly.
Yes, if you sail from the Azores, you almost have to work not to hit the Canaries.
Are the Azores in the zone of prevailing westerlies, in horse latitudes or in northeasterly trades?
Columbus, in 1493, after stopping at Azores, sailed for the embarrassing hospitality of King of Portugal. If he could have sailed southeast, passed by Algarve and go straight home to Sanlucar, would he not have done so?