The Basque side reached the Europa League last 16 last season and finished in mid-table in the Spanish top flight, with Imanol Alguacil departing at the end of the campaign.
Real Sociedad promoted Francisco from the reserve team Sanse to take his place, but La Real have won only four of 16 league matches during his time at the helm. On Friday they lost 2-1 at home against Girona, 18th, which sealed his fate.
"Current Sanse coach Jon Ansotegi will be in charge of leading, provisionally, the team into the two matches they have before the Christmas break," said Real Sociedad in a statement.
They visit Eldense on Tuesday in the Copa del Rey before a crunch league clash with Levante, 20th, on Saturday.