I would:
1. Reinstate the entrance fee, but significantly lower than the $48million it used to be, so everyone can have a shot at Formula One again, and gets at least a chance to try and convince the world they're not total, er, rejects. (Of course, this will attract many rejects, which is good.)
2. Bring back pre-qualifying under the old system.
3. Modify the qualifying format slightly so that now ten cars will be eliminated after each qualifying session. No need to increase the duration of qualifying sessions! Lots of traffic, chaos and madness, causing mixed grids every race!
4. Allow engine manufacturers that have a works team to supply three other teams, and engine manufacturers that don't have a works team to supply a maximum of five teams. (McLaren-Mercedes doesn't count as a works team.)
5. Restrict the calendar to a maximum of 18 races per season, booting out all the races on boring tracks first, then all the non-traditional ones. Force at least 50% of the races to take place in Europe.
6. Ban all winglets, flaps etc. on the bodywork of the cars.
7. Commission a cheap KERS system to be designed that every team can choose to buy (or not) at a price that doesn't hurt their budget.
8. Allow manually adjustable front and rear wings.
9. Encourage teams to run colourful, non-boring, distinctive liveries.
10. I don't really know what to put here, but I didn't like to have 9 items in my list, so I put a tenth one. Oh wait, I just remembered, I can't leave Vanuatu off the calendar, of course. Commission someone other than Hermann Tilke to design a circuit around the volcano on Tanna, or if this is not feasible, the largest non-vulcanic mountain he can find. Also, allow only a maximum of 40% of tracks to be designed by Hermann Tilke.
As you can see, most of my - I'm just going to brag and call them "improvements" - improvements are geared mostly toward the small, independent team, which will make me "The People's President", and make me very popular among fans.