Adenosine is a nucleoside that is widely distributed in the central nervous system and acts as a central excitatory and inhibitory neurotransmitter in the brain. The protective role of adenosine in different pathological conditions and neurodegenerative diseases is mainly mediated by adenosine receptors. However, its potential role in mitigating the deleterious effects of oxidative stress in Friedreich’s ataxia (FRDA) remains poorly understood. We aimed to investigate the protective effects of adenosine against mitochondrial dysfunction and impaired mitochondrial biogenesis in L-buthionine sulfoximine (BSO)-induced oxidative stress in dermal fibroblasts derived from an FRDA patient. The FRDA fibroblasts were pre-treated with adenosine for 2 h, followed by 12.50 mM BSO to induce oxidative stress. Cells in medium without any treatments or pre-treated with 5 µM idebenone served as the negative and positive controls, respectively. Cell viability, mitochondrial membrane potential (MMP), aconitase activity, adenosine triphosphate (ATP) level, mitochondrial biogenesis, and associated gene expressions were assessed. We observed disruption of mitochondrial function and biogenesis and alteration in gene expression patterns in BSO-treated FRDA fibroblasts. Pre-treatment with adenosine ranging from 0–600 µM restored MMP, promoted ATP production and mitochondrial biogenesis, and modulated the expression of key metabolic genes, namely nuclear respiratory factor 1 (NRF1), transcription factor A, mitochondrial (TFAM), and NFE2-like bZIP transcription factor 2 (NFE2L2). Our study demonstrated that adenosine targeted mitochondrial defects in FRDA, contributing to improved mitochondrial function and biogenesis, leading to cellular iron homeostasis. Therefore, we suggest a possible therapeutic role for adenosine in FRDA.