Portulaca oleracea L., commonly known as purslane, is a weed with worldwide distribution and considerable medicinal uses due to its high levels of phytochemical compounds. However, until now, few studies have been conducted on the biochemical characterization of P. oleracea grown in Tunisia, a possible area of its origin as other North African countries. Therefore, the aim of the present study was to determine the phytochemical composition and antioxidant potential of leaves and stems from a Tunisian spontaneous population of purslane. Particularly, samples were analyzed for their proximate composition, pigments, and volatiles, whereas ethanolic and aqueous extracts were evaluated for their composition in phenolic compounds and in vitro antioxidant activities. Stems showed higher content of moisture (89.9%) and anthocyanins (4.61 µg g−1 dry matter, DM), whereas leaves revealed higher chlorophyll concentrations (7.42 mg g−1 DM). Significantly higher levels of phenolic compounds and antioxidant capacities (p < 0.05) were obtained in ethanolic extracts, compared with water extracts, irrespective of the analyzed plant part. A high antioxidant activity of stems was obtained, especially when extracted with ethanol. Headspace gas chromatography-mass spectrometry (GC-MS) analyses revealed six volatile classes with monoterpene hydrocarbons, oxygenated monoterpenes, and non-terpene derivatives as the highly represented compounds. Limonene (17.3–32.2%), carvone (38–46%), 2,6-dimethylcyclohexanol (2.2–6.4%), and nonanal (3.4–3.8%) were the most abundant volatiles. Based on the results of the present study, Tunisian purslane should deserve major consideration as an edible vegetable due to its richness in phytochemical compounds and, hence, for its potential health effects.