Is Forrest Jr. actually Forrest's son?

There are probably a lot of opinions about this. My opinion is that he is.

But one thing I am sure of is that there are two clues in the movie. Their inclusion into the movie plot indicate that the creators wanted you to conclude that Little Forrest is in fact Forrest's biological son.

When Forrest first finds out about being a father, he asks if he can be with Little Forrest. He goes over to him, sits down, and they both start watching TV. From that point on their actions are identical: They get caught up in the show at the same time, AND they tilt their heads slightly to the left at the same time.

Later on, we see that they both love the same things naturally. Little Forrest loves to fish. Once again they get caught up in the sitting "action" of fishing with their heads tilted slightly to the left.

Please observe this YouTube clip that shows the father and son tilting their heads to the left. Forrest, the father, goes to his son at around 4:20 minutes; they tilt their heads at around 4:38 minutes.

In this YouTube clip, we see at 1:11 minutes that Little Forrest has a knack for ping pong. At 1:18 minutes, both father and son are fishing and again have their heads tilted slightly to the left.

She says he is...and she loved Forrest too much to lie to him about that.

I found this related answer (by sanpaco) which includes an excellent excerpt from a character study of Jenny.

"Jenny always loved Forrest, during the whole fucking movie. She loved him so much, she thought she was taking advantage of him and ran away for his sake. She didn’t realize she was wrong until it was almost too late.”

I can agree that he is his son because Forrest Jr. is about 3-4 and remember Forrest was running for 3 years.. so the time line makes sense. However, I believe it could go both ways.. Because Jenny told Forrest she had some kind of virus (implied that it’s HIV) and she knows she’s going to die and Forrest Jr. would be left in this world alone. Because if she knew she was pregnant why wouldn’t she have told him any sooner?

I do not know for sure.

There are indications that the boy is really his son.

However, this post in 9 gag suggest otherwise

https://9gag.com/gag/av5NAGd

It seems that Jenny says the same thing to all the men.

Another theory is that because Forest accept him as his son than the boy is his son irrelevant of whether he is the biological father or not.

In that case, the boy is his son only in that sense.