How does the SIM determine future player budgets? I want to resign a player to a nominal $3.6M for Season 30, but can't because I will be over Season 30's (were in 29 WS right now) player payroll budget.

My finance page says I have $87,050,000 allocated for this past season and 69.600,000 for next (Season 30).

I've currently committed $67,295,000 for next season.

From the "Help" for the "Franchise Payroll" page:

Budget Information, Player Payroll Budget - This captures your current budget status. The player payroll figure represents the amount that you have allocated to your player payroll +/- any transferred cash from trades. The amount that you may allocate to future seasons is reduced by 80%, 70%, 50% and 50% in order to prevent trashing a franchise for the future. You may not allocate more than this payroll budget for any season.

I have player thats a free agent next season and I wanted to give him an extension at the end of this season. Due to the future budget constraint, it looks like i wont be able to (I havent tried it yet). He's asking 6.5m, I'm capped at 66.4M and already at 64.6M for next season. Will he still give me a chance to resign him before he hits free agency at the beginning of next season?

Hardball Dynasty – Fantasy Baseball Sim Games - Player Profile: Jesse Blowers

Yes, because you will set a new "current season" payroll budget for next season at that time.

If I'm understanding the question correctly, "probably."  It is possible he will decide in the offseason that he's testing the market no matter what, but I think that's uncommon for a player that will sign with you at this time.

Blowers will resign, due to his 98 patience