This cross-sectional study aimed to identify the patient characteristics and clinical test results that predict the functional gait speed of people with Parkinson’s disease (PD). The impact of dual tasks on gait in Parkinson’s disease (PD) reveals a lack of automaticity and increased cognitive demands. We explored which characteristics explained walking speed with and without dual-task interference and if they reflected the cognitive demands of the task. The preferred gait speed, stride length, and cadence were measured in individuals with PD through five conditions: single-task (ST) and visual, verbal, auditory, and motor dual-tasks (DTs). Sociodemographic and disease characteristics and the results from clinical tests such as the Dynamic Parkinson’s Disease Gait Scale (DYPAGS), Frontal Assessment Battery (FAB), and Parkinson’s Disease Questionnaire-39 (PDQ-39), among others, were also recorded. Two models of multiple regression analysis were used to explore the predictive value of outcomes concerning speed. In Model I, clinical results were included, and in Model II, spatiotemporal variables were added to the significant predictors of Model I. Forty PD patients (aged 66.72 (7.5) years) completed the assessments. All the models generated were significant (p < 0.01). Models I and II accounted for 47% and 93% of the variance, respectively, in the single-task condition. A patient’s gender, prescribed medication (drugs), academic level, and Hoehn and Yahr (H&Y) stage, along with the FAB, DYPAGS, and PDQ-39 scores, were significant predictors of gait speed in Model I for the ST and DT conditions. In Model II, the H&Y stage and prescribed medication (drugs), along with the FAB and DYPAGS scores, remained significant predictors. This research found that sociodemographics, the patient’s stage disease, and their clinical test results contribute to their walking speed, highlighting the multifactorial nature of gait in demanding environments.