Mulch would certainly stop plants from self seeding. Once the plants go to seed, pull the mulch away from the plants to improve chances of reseeding. Other plants that reseed are marigolds, calendula (pot marigold), pansies or violas, sweet william (wonderful for fragrance), nigella (really nice ferny foliage), carnations, zinnias. I'm sure there are lots of others. Personally I do not grow Forget Me Nots anymore because the plant dies right after flowering, for me anyway. I grow Jack Frost Brunnera, Chinese Forget Me Not. It flowers about the same time, reseeds, and has lovely foliage after flowering. Hope this helps. Marg

For-get-me-nots are biennial so you need to seed them two years in a row to get them to reseed and flower reliably.
I do not have mulch where I grow them.
Caroline

rose campion and columbine are great re-seeders along with echinaceas and gaillardias and foxgloves.

I had some FMN that did well last year. I saved a ton of seeds and tried to germinate them this year. Not a seed sprouted, BUT the seeds leftover from last year (the original pack) did sprout.

I think it's the fact that they were from McKenzie's and must have been GMO.

This year I had tons of forget-me-nots that bloomed in my front yard. After blooming and when the seeds have formed and dried on the plant, I remove the plant totally, turn it upside down and give it a shake. This allows for the seed to fall out. In time seedlings will emerge. I then thin them out as they grow, and when they are large enough, I transplant them where I want them to be next year. I believe that biennial means that the seedlings require two seasons growth, and in this case, you need to grow the seedlings one year in order for it to bloom the next year.