There is no bad time to seek cheap flights to Carcassonne. The sun shines almost year round. Temperatures during spring and autumn are mild, perfect times for short breaks.
Peak Season:
The summer months, April to September, are peak season. This is when most tourists throng the medieval city and when most second-homers arrive.
Off Season:
October to March is officially the low season. Some attractions have shorter opening hours during these months.