This research examined the association between the risk of falls and cognitive function in older individuals at risk of mild cognitive impairment. One hundred seventy-five older adults were included in 2021. Balance confidence was scored using the Activities-Specific Balance Confidence Scale (ABC), gait speed was assessed by the 4 m test, handgrip strength by a digital dynamometer, and balance by the Timed Up-and-Go Test (TUG). The Mini-Mental State Examination (MMSE), The Controlled Oral Word Association Test, and The Boston Naming Test short-version questionnaires assessed global cognitive function, verbal fluency, and language, respectively. A bivariate correlation analysis and multivariate linear regressions were applied, adjusting for confounders (BMI, sex, age, and educational level). Shorter time in the TUG and greater educational status were independently associated with improved scores on the MMSE. Lower age and greater educational status were independently associated with increased phonological fluency. Better ABC and performance on the TUG and higher educational attainment were independently associated with enhanced semantic fluency. Higher education level and gait speed were independently associated with increased language (all p < 0.05). Improved physical factors, such as gait speed, grip strength, balance, and balance confidence enhanced cognitive function, particularly global cognitive function, verbal fluency, and language, in individuals over 60, with education as a potential confounder.