I can answer you from the Shia perspective.
According to the Imami school which is the Shia school of theology, human accountability for his deeds and Divine compensation for them are necessary features of Divine justice. And for human responsibly and Divine compensation to be fairly possible, there must be free will. So denial of free will logically negates the said responsibility and compensation which in turn undermine Divine Justice which is a key article of Shia faith. Of note, denial of Divine justice also entails denial of other attributes such as Compassion and Wisdom that in fact constitute Divine justice, all of which are in violation of "Monotheism in Attributes" (tawhid us-sifat, Arabic: توحید الصفات) according to Shia conception of Monotheism, which divides this key doctrine of Islam into four spheres: Monotheism as in 1) essence, 2) attributes, 3) acts and 4) worship. Monotheism in attributes is the belief that Allah embodies all attributes of perfections (such as, compassion, wisdom, justice, power, etc.) and that He is the origin of all good attributes in creation.
But deciding the status of a person who denies a doctrine of religion is a bit sophisticated. Apart from denial of Monotheism and Prophethood which is a definite indicator of kufr, verification of kufr with respect to denial of the lesser doctrines of religion depends much more on evaluation of the subjective conditions of the denier rather than the necessary logical implications of denial.
According to Shia fiqh, if some who denies a lesser Islamic doctrine such as free will realizes that his denial leads by logical consequence to denial of Monotheism and/or Prophethood but insists on the denial, he will be a kafir, but if he denies it without/before affirming or knowing about its ill consequence for basic faith, he will be still counted as a Muslim.
I used this entry from wikifiqh.ir (a Farsi encyclopedia on Twelver Shia Jurisprudence) as a source for the part on verification of kufr.
A note on Imami understanding of free-will
Regarding Shia understanding of free will. This notion is understood differently than in other theological schools such as Ash'arite and Mu'tazilite.
A well-known maxim of Imami theology which was mean to transcend the dichotomy of delegation (تفویض) vs compulsion (جبر) that divided the Mu'tazilites and some early Ash'arites was that truth is neither of the position but "something between the two". (Arabic: امر بین امرین). This was what Imam Jafar us-Sadiq reportedly said to an inquiry about the position of the Prophet's Ahl al-Bayt with respect to the mentioned controversy. The statement of Imam Sadiq was meant to suggest that humans are neither absolutely free and sovereign in their actions nor compelled by Allah into doing things they do; that there are things that humans can freely affect owing to their relative free will and things that they don't have control over; and that human responsibility is judged based on things that have been within his power not outside it.
Sources for more study
There are many brilliant works by Shia scholars that extensively discuss the topic of free-will within Islamic theology and philosophy, in which the basic meaning and full nature of free-will is consequently elucidated, but as of yet there are only a handful of them available in sound English. From a few works that I checked, I found two of them to be properly translated and readable that I think address your particular question:
- Lessons 18 to 20 from Lessons on Islamic Doctrine, Book 1 by Sayyid Mujtaba Musavi Lari brilliantly translated by Dr. Hamid Algar.
- This part from The Causes Responsible for Materialist tendencies in the West, one out of a few dozen masterpieces authored by Ayatollah Murtadha Mutahhari, one of the most intellectually and socially influential Shia scholars in recent history.
