The current study used quantitative electroencephalography (qEEG) to characterize individual differences in neural rhythms at rest and to relate them to fluid reasoning ability, to first language proficiency, and to subsequent second language (L2) learning ability, with the goal of obtaining a better understanding of the neurocognitive bases of L2 aptitude. Mean spectral power, laterality, and coherence metrics were extracted across theta, alpha, beta, and gamma frequency bands obtained from eyes-closed resting-state qEEG data from 41 adults aged 18–34 years. Participants then completed 8 weeks of French training using a virtual language and cultural immersion software. Results replicate and extend previous studies showing that faster learners have higher beta power recorded over right hemisphere (RH) electrode sites, greater laterality (RH − LH/RH + LH) of alpha and beta bands, and greater coherence between RH frontotemporal sites across all frequencies, although only coherence measures survived multiple comparisons. Increased coherence within and between RH networks was also associated with greater posttest declarative memory scores and with more accurate speech during learning. Total speech attempts, in contrast, correlated with bilaterally distributed small-world network configurations, as indexed by lower power and coherence over high-frequency (beta and gamma) bands recorded over frontotemporal networks in both hemispheres. Results from partial correlations and regression analyses suggest that the neural predictors of L2 learning rate, posttest proficiency, and total speech attempts varied in their degree of overlap with qEEG correlates of first language proficiency and fluid reasoning abilities, but that neural predictors alone explained 26–60% of the variance in L2 outcomes.