Teaming up with a monarchy while making a stand against royalty and hereditary power seems a little contradictory. Did any key members of the War of Independence voice concern over tarnishing one of the principles behind the war?
I've read that some of the Founding Fathers advocated for a monarchy-like system when designing the US government, is it more accurate to say they were specifically against the British monarchy and their specific situation, rather than the concept overall? (Thereby not having an issue with France having a King.)
It's important to remember that most of the Founding Fathers were staunch lifelong monarchists. It took a really long time and a lot of rebuffs and basically ignorals from King George and Parliament before they decided that the only solution would be the Declaration. Even after many had reached this realization there were others who opposed it, even within the Continental Congress.
France was a natural and historic enemy of England, and their offer of financing and troops likely swung the war in favor of the Continentals. Franklin and Adams themselves were sent to France for many years to build a strong relationship between the Continentals and later the US with France. Franklin adored the French and Adams appreciated their assistance but received something of a culture shock when he was serving there.
In any case, your question specifically asks about the opinion towards monarchies. In general, the Founding Fathers were not anti-monarchist by nature. As you pointed out, there were various proposals on what the new American government might look like and a more distributed monarchy was considered.