I was reading about the emperor Charles V of Austria and his rivalry with Francis I of France, and how though his election as HRE was likely a near certainty, he was still apparently in competition with both Francis I and Henry VIII of England.
I know that for much of the later period of its history, the imperial crown was almost a hereditary possession of the Habsburgs due to their power and commanding position in the empire. But at any point in its history, did the electors ever actually choose monarchs or nobles from outside the empire itself?
What impact would this have had on the HRE? Would it have made diplomacy difficult for someone like the French or English king to ostensibly be the defender of the empire and the commander of the imperial armies? Would elements of the empire itself (like the Habsburgs) have resisted the election?
do you mean "ruler from outside the empire" or "person who came from a family outside the empire? Otto IV seems like an example of the latter. Otto was Matilda's son (Henry II and Elanor of Aquitane's daughter/Richard the lionheart's sister), and it was part of a major civil war in the empire as the northern princes (and the pope) opposed the Hohenstaufens lead by Phillip of Swabia (also crowned emperor). Otto barely won the war (phillip was assassinated) and became sole emperor. He broke his promises to the pope about keeping the HRE and sicilian crowns separate, conquered southern italy but lost in the long run as fredrick II (then the minor king of sicily) ascended to the throne after he was deposed by the pope and a rump southern german contingent.
The French supporter Fredrick's claim (and got the majority of the germans to elect Fredrick a second time) which prompted John to intervene via and invasion of France with Otto. They lost at Bouvines which also saw the British realistically loose all hope of getting back their french lands (thus magna carta later).
as this horribly written summary shows sometimes the empire looked for unlikely candidates and it could turn into a real mess. The outsider only got elected because there was dissatisfaction with the ruling faction in the empire which pretty much ensured conflict. Helping that out was the fact that imperial politics were very messy with struggles by and against the emperors for power (with popes liberally weidling excommunication powers).
Would it have made diplomacy difficult for someone like the French or English king to ostensibly be the defender of the empire and the commander of the imperial armies?
so nothing this extreme ever happened (well you might argue Otto I) but electing a relative of a foreign king did bring in diplomatic tensions with other rulers for obvious reasons.
the habsburgs also briefly lost the crown during the reign of maria theresa as pretty much everyone turned against austria and repudiated the pragmatic sanction. However, a wittelsbach (bavaria) took the throne so that's not really outside the empire (though austria did pretty much take over bavaria at this point
I can't think of any other than Charles V of Spain/Naples/Austria/Spanish Netherlands