Will a 1986 3.8 Mustang engine fit in a 2001 mustang?

It should they are the same block. The issues will lie in the electronics of the 2001 mustang. You will most likely get a check engine light. They both use different transmissions so you would either have to swap trannys unless you have a manual.

Thanks Austin, We were gonna change the carb to the fuel injection if possilble. Its an automatic, But I have the auto trans with the 86

Then you should be good to go

You will need the computer and engine wireharness from the 2001. You would be better of using one from a 98 unless you plan on converting your system to a returnless style fuel system(one fuel line to engine, no return). Anything is possible, just make sure you cover all your bases in respect to which sensors will need to be turned off in the computer programming. I converted my 98 3.8 AODE (4r70w) to a T5 standard many years ago with ease, just needed to get the programming right.

Also, although the blocks are similar, the castings are completely different. Internally everything is very different and the 01 is Neutrally balanced and yours is EXTERNALLY balance. My main suggestion to you is to join a Mustang forum(v6mustang.com) or equivalent and pick the brains of those who have already attempted this swap.