Its possible the freeze did kill the seeds. Most of teh time its not worth the effort to connect the herb seeds like basil as they are usually grown in a specific environment for seed production. Give them at least 2 weeks of indoor temps. Here is another question- You probably you have seen dill sprout the next year when you allowed the dill to go to seed. Also, true with coriander seeds. They do survive winters as do some tomato seeds. Basil, on the other hand has never been seen the following year even after its had a lot of seeds that drop into the soil. The seeds are not THAT small, compared to something like portulaca seeds that are smaller than salt grains. Basil seeds are usually black. I like starting from store bought seeds. That way, I am sure that I am getting some strains of basil and other herbs that are going to do well, as opposed to collecting seeds. The opposite is true when I like a tomato type, where I save as many seeds as I can. I also save seeds from some of my asparagus plants (Mary Washington) and these do very well when started indoors in March, and transplanted nearby my established asparagus plants.

Basils need warmth to germinate & thrive. Not to worry, most all basil seed is relatively inexpensive and widely available.

Can't speak for basil, but some kinds of seed need after-ripening. There is a lag time needed from harvest to planting.