Some armours gave reasonable groin protection, but very few provided thorough groin protection - Henry VIII's "space suit" armour is exceptional in its level of groin protection. Groin protection would come from a combination of armour, stance, shield, and active defence by parrying or getting out of the way. Against many weapons, a kick has less reach, and simply not letting the opponent get close enough will provide good defence against kicks to the groin.
Generally, the groin was not off-limits for attacks. The main problem was not kicks, but thrusts/stabbing with weapons. For example, if the armour being worn was a mail shirt covering the upper thighs, a stab upwards into the groin would bypass the armour. Also, a stab to the groin is much more dangerous than a kick to the groin. Apart from the general principle that a stab wound is more dangerous than a kick, stabs to the groin can easily hit large arteries such as the femoral artery, causing rapid unconsciousness and death.
Various European martial arts manuals ("fight books") include groin attacks - usually with weapons. Some examples:
Take out his incoming thrust with the short edge from the changer strongly, upwards, so that your weapon flies around in the air, into the right Ox, and Instantly throw him a thrust from under through the right plow, to his Groin or forward positioned thigh.
When one thrusts to you from below, so step with the left foot to his right side and set his thrust from your left against your right from above, between you and he, through to the Bastian, step and thrust him under his weapon into the Groin.
When one cuts an undercut from the right onto your sword and winds at the same time the thrust under to your groin, then cut at the same time as the thrust with a footcut sideways from your left to your right. At the same time, quickly step to his right, and wind the point to his groin. Thus you do to him what he wanted to do to you.
Meanwhile wind your blade upwards over his from below, with the point to his groin.
Cut a high cut to loosen him but don’t let it hit, pull around and stab him in the groin from below.
Fiore de'i Liberi includes kicks to the groin in his techniques:
In unarmed fighting: I will strike you so hard in the groin That all of your strength will be taken away. This student strikes his opponent with a knee to the groin to gain advantage in order to throw him to the ground. To make the counter, when your opponent comes in quickly to strike you in the groin with his knee, seize his right leg under the knee with your right hand, and throw him to the ground. https://wiktenauer.com/wiki/File:Pisani-Dossi_MS_05a-f.png
When fighting with swords: When I am crossed with someone and come to the narrow, I strike his testicles with my right foot. This play, where I strike you with a kick to the groin, is made to hurt you so much that your cover will falter. When you make this play you should do it quickly, to prevent your opponent from being able to counter it. https://wiktenauer.com/wiki/File:Pisani-Dossi_MS_20b-b.png
Hans Talhoffer also includes a knee to the groin in wrestling:
