This paper lays out a pilot study conducted to examine the roles of Cross-Linguistic Influence (CLI) and cognitive resources on processing and parsing in a second language. The present study builds upon one conducted by Andersson et al. (2018) investigating behavioral and electrophysiological (EEG) responses to syntactic violations in a first or second language. The main goal of the previous study was to investigate whether the presence or absence of a syntactic feature (in this case V2 word order) would predict electrophysiological and/or behavioral responses to syntactic (word order) violations in the second language. The study found that while +/-V2 in the L1 did not seem to influence behavioral data, it did show some influence on the EEG results. The goal of the present study is twofold. We seek first to replicate the previous online and offline results found in a-V2 population, and then investigate the role of linguistic and cognitive variables in modulating the anticipated effect. We show that the same effect demonstrated by the-V2 participants in Andersson et al. (2018) is borne out in our French participants in the form of an anterior P600 effect. Furthermore, our data show a relationship between offline measures of cognitive functioning and online responses to linguistic stimuli. This work has implications for our understanding of cross-linguistic influence in L2 acquisition, as well as the role of domain general cognitive functions in processing language.