I was studying West Civilization and other events in history and I was quite conflicted here. I know who Louis was and everything but I don't really know enough to be able to answer the question in depth. So what effect did his death actually have in regards to the French Foreign Policy?
The foreign policy of France remained largely unaffected. Revolutionary France continued its agressive foreign policy against the monarchies of Europe in an attempt to spread the revolution, leading to the continuation of the French Revolutionary Wars. The execution of Louis XVI outraged monarchs across Europe, making them even more antagonistic towards the revolutionary regime in France than they had already been and rallying them against France in the so-called First Coalition.
As a direct effect, Great Britain expelled the French ambassador in reaction to the execution, which prompted France to declare war upon Great Britain (and its ally the Dutch Republic).
Overall, the execution of Louis XVI marked a point of no return for the revolutionary regime. They knew there could be no more reconciliation with the powerful European monarchs after this, so they became more radical and agressive in pursuit of the spread of their revolutionary ideas abroad. The French Revolutionary Wars had already been ongoing, but things escalated quickly after the execution of the Louis XVI.