The Royalists did receive some limited assistance from continental Europe, but it was mostly limited to supplies of arms from the Netherlands and France. Unofficially some Europeans joined in the civil war from mostly mercenary motives. Their numbers were extremely small and they'd barely be worth mentioning were it not for the squadron of Royalist privateers commanded by the Dutchman Jan Van Haesdonck, which was the only significant foreign force involved that I can think of.

The lack of greater intervention from continental Europe was probably down to a number of factors.

The reaction to Charles I's attempt to bring Irish troops into England to fight against his own countrymen tells us something about how the idea of using foreign troops in a civil war was perceived at the time. Charles was vilified for trying to bring foreigners into the country to kill Englishmen, and they were foreigners over whom he was ruler, one can only imagine the reaction to non-British foreigners would have been similar or worse.

Most European countries, if they had an interest, were supporters of the Royalists, but the English navy was more of less totally under the control of the Parliamentarians. The navy was not as powerful in the 1640s as it had been (or would become), but it was still formidable and sending an invasion force without control of the sea would have been foolhardy.

Thirdly, most of Europe was embroiled in the 30 Years War, so had little to offer by way of assistance in a sideshow in the foggy island to the North.