We have obtained ALMA Band 7 observations of the FU Ori outburst system at a 0 ''.6 x 0 ''.5 resolution to measure the link between the inner disk instability and the outer disk through submillimeter continuum and molecular line observations. Our observations detect continuum emission that can be well-modeled by two unresolved sources located at the position of each binary component. The interferometric observations recover the entire flux reported in previous single-dish studies, ruling out the presence of a large envelope. Assuming that the dust is optically thin, we derive disk dust masses of 2 x 10(-4) M-circle dot and 8 x 10(-5) M-circle dot for the north and south components, respectively. We place limits on the disks' radii of r < 45 AU. We report the detection of molecular emission from (CO)-C-12(3-2), HCO+(4-3), and from HCN(4-3). The (CO)-C-12 appears widespread across the two binary components and is slightly more extended than the continuum emission. The denser gas tracer HCO+ peaks close to the position of the southern binary component, while HCN appears to be peaked at the position of the northern component. This suggests that the southern binary component is embedded in denser molecular material, consistent with previous studies that indicate a heavily reddened object. At this angular resolution, any interaction between the two unresolved disk components cannot be disentangled. Higher-resolution images are vital for understanding the process of star formation via rapid accretion FU Ori-type episodes.