A few reasons. Firstly i believe you are confusing the July Revolution, which did not establish a Republic but rather brought to power the more constitutional July Monarchy of Louis Philippe I, with the later French component of the revolutions of 1848.

As to why they did not intervene in the July revolution it was for a number of reasons. Firstly as i said Charles X was allowed to peacefully head into exile to be replaced by his cousin Louis Philip making the July Revolution both a less politically radical and a lot less bloody in general. Secondly because where the French revolution dragged on over an extended period of time. The start of the serious political resistance and then violence occurs over the summer and autumn of 1789. It is not until 1791 when Louis XVI safety is becoming more seriously in question when the Prussians and Austrians begin make formal declarations to defend Louis. France is not invaded until 1792. Louis is not executed until 1793. In contrast, the July revolution was done in a short working week. By the time anyone could have considered intervening it was a fait accompli. Additionally, the Napoleonic wars were still pretty fresh in everyone's mind. No one was especially enthusiastic to going back to that conflict. And Charles X hadn't inspired that much enthusiasm, while he had been a political ally of Britain i think it was widely recognised he'd very much brought the July revolution on himself and Britain itself was a relatively liberal monarchy so they didn't actually dislike the form of constitutionalism that Louis Philippe produced.

As for the revolution of 1848 thats largely because much of europe was busy. Two of the other four great powers in europe, Austria and Prussia, had their own revolutions going on that year in addition to ones in Italy and the other German states. Of the two other great european powers of the day Russia was slow to react and had the more immediate revolutions in Hungary as a priority. And of course Russia is far away and the French component of the revolutions of 1848 was already over by march 1849 when the Russians began moving.

Britain meanwhile was operating a relatively small army at this time and simply had little interest in becoming involved in any significant continental conflict.