What's complicating this issue is that the adverb "just" has several distinct meanings that could apply here.
The meaning you're presumably asking about is "moments ago, recently".
In this sense, *"I just see" is ungrammatical; "just" in this sense implies that the action occurred in the past, which contradicts the present tense "see".
You can say either "I just saw" (past simple) or "I've just seen" (present perfect); there isn't much difference in meaning between them, since in any case, "just" fixes the time of the event to the recent past. There's a slight difference in emphasis, but in most cases, expressions like:
"I just saw the movie."
"I've just seen the movie."
are basically interchangeable.
You can also use "just" with the present progressive tense to mean "currently, right now", as in:
"Call me back later, I'm just watching the movie."
This usage is not (yet) mentioned in the Wiktionary entry linked above, but e.g. The Free Dictionary does list "at this very instant" as one of the definitions of "just", with the example sentence "he's just coming in to land."
This may well be the meaning you were aiming for with *"I just see", although one would not usually use the verb "see" in a progressive tense (except in some secondary senses of it, such as "waiting to observe an outcome" or "being involved in a relationship with"). Normally, one would instead say e.g. "I'm just watching <something>" or "I'm just looking at <something>".
Just to confuse things, however, an alternative meaning of "just", which could also apply to your examples, is "only, simply, merely":
"I just saw a basketball game. I didn't see any gorilla."
"I just see an error message. I don't see any way to get rid of it."
What using "just" in this sense, especially with a verb in the past tense, it's often more natural to place it after the verb to make it less ambiguous:
"I saw just a basketball game. I didn't see any gorilla."
This isn't always possible, however, since it does change the meaning a bit: when placed before the verb, "just" (in this sense) applies to the whole action, whereas after the verb it only applies to the object. For instance:
"I just saw the dead rat, I didn't touch it."
is correct, whereas:
*"I saw just the dead rat, I didn't touch it."
is not; it's clear from context that "just" should be modifying the verb "see", not its object. In such cases, to avoid confusion with the other meanings of the word "just", it may be preferable to replace it with some other synonym, such as "only".