Certainly.

This fear was such, that, early on, a non-intervention agreement was signed by many European countries in August of 1936, which created the aptly named Non-Intervention Committee. The most vocal parties for non-interventionism were the French and British. While Italy and Germany were on the committee, they openly flaunted the agreement and guidelines, sending volunteers, aircraft, tanks, and material to Franco's Falangists. The USSR was also on the committee, and it to, ignored the prescription of non-interventionism, sending military aid to the republicans.

Britain and France did, on the whole remain loyal to their pledge of non-interventionism, though France covertly donated planes and specialists to the Republicans.

So yes, the conflict was met with a fear of it spiraling into a wider war, and while on paper, the major European powers pledged non-interventionism, many of these broke it.

To expand somewhat on the previous answer, I think this is one of those questions where it is really important to stop for a moment and think about whose perspective we are thinking about.

There was certainly concern on the part of the British Government that a proxy war in Spain might lead to a broader conflict between fascist and democratic powers. This led to their proposed solution of Non-Intervention, which they were able to persuade the other major European powers to agree to (but not, as mentioned previously, to stick to). This raises another interesting question though – in breaking the Non-Intervention Pact, did Hitler or Mussolini think they were risking a wider war? Would they have been willing to push intervention so far in the face of determined opposition? This starts to get into speculative territory, but it’s worth noting that depending on which European government’s perspective you take, the degree of ‘fear’ was rather different.

To my mind, the question gets even more interesting when we consider the problem not just from the perspective of governments, but their citizens. In Britain, whose government was Non-Intervention’s most ardent supporter, the Republican side was considerably more popular than the Nationalists, and there was considerable opposition to Non-Intervention, and a great deal of political and fundraising activity in support of the Republic. Aid Spain, as it became known, was probably the largest sustained international solidarity campaign in modern British history, raising the contemporary equivalent of tens of millions of pounds for the Republic. Most famously, about 2,300 volunteers left Britain to fight in the International Brigades (who in turn were made up of about 35,000 mostly European volunteers) – clearly, these individuals did not fear the potential breakdown of peace as a result of their actions. In fact, they and their supporters saw the debate differently – that by allowing the Spanish Republic to be defeated, fascism would only be strengthened and emboldened, making a European war all the more likely. Many British International Brigade volunteers, both at the time and ever since, claimed that they went to prevent the Second World War from happening in the first place.

How far was this view shared? In one of the first ever issue-based opinion polls in British history (that I’m aware of), 57% of British respondents claimed to favour the Republic in October 1938. By January 1939, this had increased to 72% supporting the Republic. This number has been cited to show the extent of support for a reversal of British policy on Spain, although to my mind it is a bit more complex. For one, the dramatic shift over a short period – especially so late in the war, seems to indicate that these numbers might be soft. More fundamentally, the question was not whether Britain should intervene, or even change their policy, but simply which side they preferred. So, it’s hardly definitive evidence that the British people were either willing to risk war over Spain, or that they believed there was no such risk. But it does certainly indicate that the answer to your question is going to look quite different depending on whose views you are interested in.

Other answers above have discussed the approaches by other powers to limit intevention and to stop the conflict from spreading. I am very interested to hear about the impact internally in other countries.

Specifically what was the impact internal to France? After all superficially it has similar internal political and social problems and shares a border. I presume it further divided the country at a time of a similar popular front government facing reactionary forces.