Yes. While there are many cases, France is a good example. If you look at figure 1 of this paper you'll see that in the post-WWII era the communist party got over 25% of the votes in national elections, which is plenty to have a significant effect on policy. As of 1995 that was down to about 10%, but that's still not a fringe party. Compare that to the US, where typically no 3rd party gets more than 1% of the votes (don't worry, I'm talking pre-1995). The big exception was Ross Perot in 1992 with about 20% of the vote. However it seems to have been more about Perot than the Independent Party, as for example it won less than 1% of the votes for the House of Representatives in the same election.

While the paper I cited is largely about the decline of the communist party in France, it lists its historical peaks to make that point. For example "The PCF lost the mayorships in 23 cities in 1989 and lost an additional 200 cities in 1995." which shows that at one time communist mayors were not that unusual in France (as an American it seems surrealistic to think of a communist mayor in this country).