I'm assuming you mean Charles I and not James I?

Anyhow, I would argue there are roughly three big reasons for the different reactions to each execution.

First, the English Civil War and Charles' subsequent execution were coterminous with the final stages of the Thirty Years War on the continent. The war was devastating and had left large swathes of the European heartland shattered, as well as exhausting the financial and military resources of many of the great powers. Even if any of them had been inclined to take umbrage to the Parliamentarians' actions in England, it's not clear that they would have been in a position to do much in the wake of fighting such a taxing conflict.

Second is the political context each of the executions happened in. Charles I was dethroned, tried, and executed by a rival faction of the nobility who resented what they viewed as his overreaching and his disregard for parliament and the nobles of the realm. While the execution itself (and the trial in particular) may have been uncommon, the rest of that story would not have been unfamiliar in many other parts of Europe. I'm not an expert on what the general European attitude toward the Commonwealth and later the Protectorate was during their brief existences, and while I'm sure there would be plenty of monarchs who weren't exactly enthused about it, the fact that it was merely a group of nobles who wrested power from a king and executed him after a trial for their grievances would have made it seem far less shocking than the unruly mob and reign of terror that came to characterize much of the French revolution.

The Jacobins' dramatic overthrow of the Bourbon monarchy, in contrast, came at a very different juncture in history. It disrupted 100+ years of the development of the tenants of absolutism (which had never really taken hold in the British Isles, as it had on the continent), and in doing so it shook the very foundations underpinning many of the other great European monarchies to their core. It essentially represented an affront to the very philosophy of rule many of these kings and emperors had come to see as inviolable. The French revolutionaries were endangering not only the basic dynastic ties that bound the continent's kingdoms together (remember that Marie Antoinette was a Habsburg, the other preeminent European royal family), but also the foundational ideas upon which much of European society and political organization rested. The revolution had to be crushed and the monarchy restored because of what it represented; European monarchs were terrified at the notion of the ideals of the revolution spreading beyond the borders of France and eventually to their realms.

And the final salient point is the geopolitical implications on the continent with Louis XVI' execution, compared to the relative lack of them for Charles. The English crown's capacity to directly threaten (rather than harass) any of the great powers on the continent in 1649 was limited at best, and there was little reason for any European powers to fear negative effects from the aftermath.

The situation in 1792 was radically different. France was arguably the preeminent power on the continent, and instability and unpredictable behavior from its ruler(s) had the potential for profound consequences for virtually every other major power of the day. Other European rulers feared what a united French nation with some as-of-yet undetermined governing body's interests would be, and what it would decide to use its tremendous power and military resources to do (i.e. crush them, or as I mentioned earlier, make them a target for the spread of republicanism). As it happens, this wasn't really an irrational fear either; in the revolutionary wars that were to dominate the rest of the 1790s, the French Republic was to win a series of stunning, decisive victories against the coalitions that aligned against it and end up more powerful and stable than before the fall of the monarchy.

In short, I would say the biggest takeaway point is that while the murder a monarch wasn't something that was likely to sit well with other monarchs in most contexts, the difference here is best explained by the fact that what happened in France had a much more direct ideological and strategic impact on the rest of the continental European powers than what happened in England, so they had a much more pressing interest in reversing it, or attempting to anyway.