This achievement is a major grind but there's a few events to look out for that give good rewards.
Pick all the A class events that come up, then check your calendar to see which track they are on and how many laps. If an event has lots of races of lots of laps, you may want to skip it if you already have the collector achievement and don't need the money. You can skip an event from the career home screen by pressing X.
For races that are on both Supersport and Superbike, you only get one lot of prize money if you do both, but you will get more fans.
Once you've done a few seasons and build up fans you'll start being offered more A class events. I have found the 4 section events on Snaefell Mountain to offer the best fan reward. Most of these take from 6 to 10 minutes depending on your skill and which sections they are for.
They can be for both supersport and Superbike and I recommend doing both. I was doing sections 5-9 which took me a combined 12.5 minutes, however I crashed out a few times and came 2nd in SS and 5th in SBK. I received 8k fans for this event (was only listed as 1.5☆ fan gain). Average reward for these events was from 8-10k fans for 12-20 minutes racing.
(I'm not sure if the number of fans you get scales up as you progress, if anyone could check their results for one of the 4 section Snaefell races that would be great!)
Try to avoid the events on Antrim and Super Hillside as they are very time consuming for the reward you get. Milford Street, Old Blair Forest and Tyrone are the shortest tracks so well suited for fan farming.
If you have any specific questions fire away in the comments.
I know this isn't the best guide but I hope it helps someone on their way!