I can't talk about Prussia, but Spain's initial position was one of neutrality.

We must take into account that France and Spain had been allies for most of the 18th century and Enlightenment ideas were popular in the country, especially among the elites such as the Prime Minister Floridablanca. However, they had to deal with opposition from the reactionaries, like the Inquisition. Add political struggles, like the antipathy the wife of king Charles IV had against Floridablanca, and the situation was complicated. They were also aware of the financial crisis and other problems of the French monarchy, as Floridablanca confessed to Russian ambassador Zinoviev, so they expected some kind of trouble in 1789.

Once the revolution started the initial reaction was one of opposition. Spanish rulers were worried about the influence of revolutionary propaganda in Spain. Previous rivals like Floridablanca, the queen and the Inquisition banded together to stop it, forbidding French and Enlightenment publications, controlling the activity of social clubs and even expelling French citizens from the country.

Nevertheless, in 1790 political trouble starts again in Spain. Floridablanca starts losing his power and Spain decides to keep a neutral stance towards France. After all, there's still a king on the throne and Spain has problems with England too. While in Austria, Prussia and Russia diplomacy awaits some kind of reaction from Spain when they hear news about the French Constitution, the country says nothing.

But later events changed the situation. The king of France was arrested when trying to flee the country and then forced to sign the Constitution. Spain then starts joining the other European powers to plan actions against France. Iriarte, the Spanish ambassador to France, claims that his ruler doesn't think that the king of France was free to act and decide on his own volition, so no message signed by him could be trusted.

However, then comes a change. Floridablanca, who had supported a harsher stance against France, loses his position. Under the new minister, the Count of Aranda, Spain recognizes the French Constitution and starts again friendly relations, although they get more difficult when the Republic is proclaimed. But, again, the minister is changed and Godoy takes his place in 1792. Although he initially continues the policies of his predecessor, he adds that peace between Spain and the French Republic depends on the lives of the (former) king of France and his family.

I think you can guess what happened when they were executed.

In 1793 the confrontation between France and Spain was unavoidable. France declared war on Spain and Spain joined the international coalition against France. However, after a series of defeats, Spain made peace with France in 1795 and later allied with them, a situation that was kept for a decade until Napoleon invaded the country in 1808.

This is just a summary. For more information, I recommend this article on Russian and Spanish diplomatic reactions in the years 1789-1793. It's in Spanish, mind you: http://hispanismo.cervantes.es/documentos/volosiuk.pdf