This has been asked quite frequently here, it appears. From previous answers, it seems they were too busy with other issues to intervene, and that the foreign policy of the English Commonwealth and the French Republic were rather different. And several users have pointed out that the French Revolutionary Wars began before King Louis was executed. For further information you can read these threads:
- Following the French Revolution, the other nations of Europe were shocked and
outraged by death of Louis XVI, resulting in military intervention. 150
years prior, Charles I of England was similarly executed by his own
people, but no foreign intervention occurred. Why were the reactions so
different? by u/greyhistorypodcast, focusing on the circumstances of the French Revolutionary Wars
- Why were the reactions to the regicide of Charles I of England different to that of Louis XVI of France by u/MySkinsRedditAcct, mostly on the same subject
- Why is it that when Louis XVI was executed other European monarchies attempted to suppress the French revolution but when Charles I was executed, 2 centuries, prior at that, England was left to its own devices? again by the good MySkinsRedditAcct
- What was the French, Spanish, and Dutch reactions to the English Civil Wars? Did any of them intervene? by u/GP_uniquenamefail
- What did the foreigners think of Cromwell's commonwealth by u/StgBANZAI, focusing on the reaction in Russia
- How did other European nations respond to the Commonwealth of England following the end of the English Civil War? by u/wishbeaunash, focusing on England's neighbours Scotland and the Netherlands
- What was the reaction from other European Monarchs after the English Civil War and Charles I execution? by u/itsallrightwithme focusing on the reaction from Spain
- Why didn't the overthrow and regicide of Charles I prompt massive retaliation from other monarchs the way Louis XVI's did? by a now-deleted user mentioning among other things the Thirty Years War