This is called PP attachment ambiguity. You have a preposition phrase (PP), with Harrison Ford, and you have to figure out what part of the sentence it attaches to.
Does it attach high, to watching? If so, Harrison Ford is watching the movie with you, like this:
I'm watching with Harrison Ford.
Does it attach low, to the movie 'The Fugitive'? If so, you're telling the listener that Harrison Ford is in the movie, like this:
It's a movie with Harrison Ford.
When you have this sort of ambiguity, you have to figure out what makes sense from context. Both of these are possible, but the latter is probably more likely.
If you think the ambiguity might lead to misunderstanding, you can always rephrase:
I'm watching The Fugitive. Harrison Ford is in it.
But native speakers use ambiguous sentences all the time; if they fail to communicate, they just go back and explain what they meant. You can do the same thing, if you like.