Cochlear implantation (CI) can benefit patients with single-sided deafness (SSD) in terms of sound localization, speech understanding in noise, tinnitus severity, and quality of life (QoL). In previous studies, CI outcomes have been largely reported for SSD patients with normal "unrestricted" hearing in the contralateral ear. However, SSD patients may often have some degree of hearing loss in the contralateral ear ("restricted" acoustic hearing). In this study, we report results from a French clinical trial for CI in in SSD patients (NCT02204618). Localization, speech reception thresholds (SRTs) in noise, tinnitus severity, and QoL were evaluated in 18 SSD patients 1 year after CI. Data were analyzed for 2 subject groups according to the pure-tone average thresholds in the non-implanted ear: unrestricted acoustic hearing (UNRES; ≤25 dB HL; n = 10) and restricted acoustic hearing (RES; > 25 dB HL; n = 8). Across all subjects, localization was significantly better with the CI on than off (p = 0.005); there was no significant difference between subject groups (p = 0.301). When speech and noise were co-located (S0N0), there was no significant difference in SRTs with the CI on or off (p = 0.480); SRTs were significantly better for the UNRES than for the RES group (p = 0.005). When speech and noise were spatially separated (SCINNH), SRTs were significantly better with the CI on than off (p < 0.001). While SRTs were better for the UNRES than for the RES group (p = 0.024), the CI benefit was more than 50% greater for the RES group due to the restoration of high-frequency speech cues. Questionnaire data showed that tinnitus severity was significantly reduced (p = 0.045) and QoL was significantly improved after one year of experience with the CI (p < 0.001). Age at testing was significantly correlated with SRTs for the S0N0 condition; duration of deafness was correlated with SRTs for the SCINNH condition. There were relatively few correlations between behavioral and subjective measures, suggesting that both were valuable when assessing CI benefits for SSD patients. The present data suggest that indications for CI should be expanded to include unilaterally deaf patients who have normal hearing or mild-to-moderate hearing loss in the non-implanted ear.