I'm mainly sowing the Mediterranean species Lewis, for which the usual advice is to sow before Christmas. Seeds received after that are better saved to be sown the following autumn because 1. they will not experience the necessary conditions (a long, cool and moist period) to trigger germination and 2. being thin papery seeds are more likely to rot if left in pots for a year. It's easier to keep them in good (viable) condition in a cool dry place. So, for Med species I'd definitely keep them for sowing in October.
I have only an odd potful of species from other regions and would defer to
Maggi's advice below. I was pleased with how quickly the
F. liliacea (N. American) germinated compared to other frits - the first seedlings from that batch of sowing in mid-October and up well before Christmas.