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Rivers significantly contribute to global biogeochemical cycles; however, we have a limited understanding of how drying may influence these cycles. Drying fragments river networks, thereby influencing important ecosystem functions such as the processing of carbon and nitrogen, and associated fluxes of greenhouse gases (GHGs) both locally, and at the river network scale. Our objective was to assess, using a network‐scale approach, the lateral, longitudinal, and temporal dynamics of GHG fluxes in a river network naturally fragmented by drying. We used a closed‐loop chamber with automated analyzers to measure carbon dioxide (CO2), methane (CH4), and nitrous oxide (N2O) fluxes from dry sediments, flowing waters, isolated pools, and riparian soils, along with a suite of environmental variables, over 9 months at 20 sites across a non‐perennial river network in France. Network‐scale drying had a spatial and temporal legacy effect on GHG fluxes. On average, CO2 fluxes were up to 29 times higher from perennial than non‐perennial sites under flowing conditions. At non‐perennial sites, CO2 and N2O fluxes positively covaried with time since rewetting. In addition, CO2 and N2O fluxes at perennial sites positively covaried with the percent of non‐perennial reaches upstream, indicating a spatial effect of drying. GHG fluxes from riparian soil and dry riverbed sediments had markedly different magnitudes and covariates. This research demonstrates that drying not only has a local‐scale impact but also influences GHG fluxes at the network scale, contributing valuable insights for upscaling global riverine GHG estimates. [ABSTRACT FROM AUTHOR]