I know the Great Britain was afraid the revolution might set a bad example for them, but did they try to help the French monarchy in any way? Or, did any other country consider or attempt to take the opportunity to attack France for an easy land-grab?
Well, they certainly did, to put it very simply. There were a series of seven major wars between European coalitions and France between 1792 and 1815, during which millions died, and the old order of Europe was permanently eradicated. France decisively won the first five of these wars, and in doing so, conquered most of Europe. It was not until 1814 that France (i.e. Napoleon) was defeated, but even after what was supposed to be that final defeat, Napoleon returned to power the very next year. His renewed reign lasted only around a hundred days, but it took another brief war to remove him from power again (still a significant war, with ~60k killed in a few months). At the end of these "Coalition Wars", the French Monarchy was simply restored by the European powers. So, looking at the biggest possible picture, the European powers did intervene, and kept intervening until the bitter end, when they restored the monarchy.
But, if you're wondering why they didn't intervene initially, to stop the French monarchy from being overthrown to begin with, it's a bit more complex. For background, Europe had been fairly stable since the Peace of Westphalia in 1648, which established a new European order, ending more than a century of incomprehensibly devastating religious warfare that killed millions. By the time of the French revolution, this relative peace and stability was preserved by an alliance of three dominant European powers: France, Spain and Austria. Spain possessed a massive empire, including much of Italy, and was ruled by the Bourbon family of France, its kings direct descendents of Louis XIV. Austria possessed the Holy Roman Empire, and although it wasn't actually a centralized state that could be controlled, the Habsburg rulers possessed a massive informal empire in their own right. Marie Antoinette was actually the sister of the Austrian Emperor. So, when the revolution threatened the French monarchy, they had three significant reasons to intervene. First, it threatened the longstanding European order. Second, it threatened their own power, as they feared revolution would spread to their own lands. Third, it quite straightforwardly threatened their own family members!
To understand why they didn't intervene before it was too late, one must understand that the French revolution was not a straightforward overthrowing of the monarchy by the people. There was no civil war to join in on. It was instead a gradual process of political changes, brought about by economic and popular unrest, and initially, the monarchy was not threatened. France was in a major economic crisis, and the government attempted to reform the tax system to remove tax exemptions from the nobility. Regional "parlements", which were courts responsible for recording new laws, basically abused their position to veto these reforms, to protect the privileges of the nobility. The king therefore reconvened the archaic "Estates General", a general assembly equally representing the clergy, the nobility, and the people, in order to bypass the parlements. This was ineffective, as the nobility continued to stonewall the reforms. So, the estate representing the commoners reformed as the "National Assembly". The Assembly refused to be desolved, and, the storming of the Bastille forced the king to accept these developments, and the National Assembly became a governing body and quickly abolished the feudal nobility, the privileges of the church, and began drafting a constitution. All of this, amazingly, took place in 1789, during the very initial stages of the revolution. Even after the king infamously tried to flee from Paris to launch a counter-revolution, he was still kept on the throne under a new constitution.
The revolutionary takeover was gradual, thus, so was the alarm from European powers. But, as it became increasingly radical, the concern from Europe increased accordingly. Eventually, Austria and Prussia (the other powerful kingdom of Germany) issued a joint declaration threatening war to restore the French monarchy. The declaration was actually fairly limited, and intended to be noncommittal, but it was viewed by France (i.e., the French revolutionary government) as a threat, and France declared war on Austria preemptively. At this time, France was actually still a monarchy! But, a Prussian-Austrian commander issued a proclamation to restore the king to full power, and to summarily condemn to death any who resisted. This proclamation may have backfired, further motivating the revolutionaries, or it may have had little effect at all, but it certainly didn't intimidate the revolutionaries into submission as intended. Regardless, the king's aggressive refusal to cooperate with the legislative assembly led to a breakdown of the attempted constitutional monarchy, and he was soon arrested, stripped of all titles and privileges, and executed. This definitely did galvanize all of Europe, uniting them against France, but it didn't matter, because France's preemptive war was decisively successful, as were all further attempts to put down the revolution, and subsequently, the Napoleonic Empire, and France successfully conquered Europe. It was not until Napoleon invaded Russia and captured Moscow that the tides turned. His army was catastrophically decimated in the process, and could not recover. This directly led to his defeat by the sixth coalition. Any amateur or professional historian must wonder how different things might have been, had he not made the fatal error of marching on Moscow.
Anyway, I hope this answers your question. The whole topic is incredibly complex, and while this seems like a really long explanation, I honestly tried to simplify it as much as possible. Let me know if you have any additional questions!