> >I don't know the French name of the French horn.
> "Cor".

Well, when the rotary-valved horn came into use originally,
it was "cor chromatique" (forgive me for leaving out the
accents...), because it could play all notes of the
chromatic scale rather than just the overtone series allowed
by a natural (valveless) horn. Some noted hornists believe
that the "French" comes from the fact that English hunting
horns were small (to be held in a single hand) and
Continental horns were larger (much the size of a current
orchestral horn), and thus the national adjective to
distinguish the two. Others believe that the "French"
results from the French dominance of the Alpine region when
the hunting horn was first developed there.

Of course, I personally believe that the English called it a
"French" horn because they didn't like it much.

On the "oboe" front, most histories of wind instruments seem
to agree with the (Fr.) hautbois ==> "high wood" derivation,
although the justifications seem a bit specious. Certainly
the oboe was not the woodwind with the highest register at
the time of its first popularity...