Taoism by nature of Wu Wei and other ideas, perhaps especially those put forward by Chuang Tzu, leans more in favor of there not being actual free will. In many texts Taoism though does commonly say that we "Should" do this, "Should Not" do that so discount this claim unless we alter "Should" (/not) to "Ought" (/not)*.
Fatalism is the commonly inferred antithesis to free will and so people nearly always reject views on there being no free will as they fear and dislike the idea of fatalism. This need not be the case, however, as clearer alternatives exist. Fatalism still believes that something causes events and this half cause/effect relationship, which is still ultimately cause/effect brings us to a position not really answering anything. It is not only unsatisfactory to most is it also not a strong antithesis.
What I have seen in my own personal endeavors to answer these questions and in my readings of Taoism and Zen as they venture into these realms is that we are sensitive to events, that is all. This is a very magical and privileged vantage point on reality as we witness this unfolding show but do not direct it. It is an important place for anyone standing tight with a philosophy of Oneness such as Taoism to not allow for cause/effect, doer/done situations to enter their descriptions on reality as it is reiterated over and over that Tao does not lord over anything. If Tao does not, and we're all one, then we'd better accept that free will and cause and effect are not in perfect compatibility with Taoism.
That this universe, nature, these other people and all else appears around us and that we feel ourselves as something within all of that we are naturally in some uneasy predicament when we attempt to rectify this prickly subject. The answer though, for me at least and I don't know many who can relate their views on the subject to me, is one of magical wonder. Quite the same magic I believe Chuang Tzu and others felt when they viewed the world. We are little else than a sensitive spot in the universe. Imagining the universe as it is, large expanses of space, lumps of rock, voluminous fire balls, more space, places where chemicals mix and react, places where life dances, then we seem to be little tiny and very sensitive cells in the universal entity. We have our senses where we can touch things, touch compressions in air, touch chemical traces in the air, touch light as it bounces off things. We are also very sensitive to energy changes, emotional flows in our bodies and minds and I see that we are sensitive to Tao's flow, be that Chi or Te.
That is in fact all I believe we are and we are not entities with volition but entities who amongst sensing things that do appear to happen we are sensitive to what could happen or could have happened and in this we could, quite by comical inevitable accident be lead to believe that we are the fatalistic bystander or the doer of the acts - when we are neither.
We are a sensitive spot in the universe and we sense and feel its apparent movements. By privilege of our position we also get to seem to see and seem to interact with other sensitive entities as they too do the same.
* I'm attempting to differentiate between "should" inferring you; 'must, if possible, choose (not) to' and "ought" inferring that; 'it would be best if possible, but what can we do?'.
You can check out Ta-Wan's other musings here.