As one of the three major engines of economic growth in China, the Beijing–Tianjin–Hebei (BTH) urban agglomeration has become one of the regions with the highest energy consumption intensity. To investigate the dynamic relationships between scientific and technological innovation, industrial structure advancement and carbon footprints, panel data in BTH from 2006 to 2019 was selected, and a Panel Vector Auto-Regressive (PVAR) model was established to conduct an empirical study. The conclusions show that there is a causal relationship between the industrial structure advancement and carbon footprints, and the influence of each on the other is significant. The impact of scientific and technological innovation on carbon footprints has a “rebound effect”. Scientific and technological innovation can accelerate the process of industrial structure advancement. Carbon footprints have a significant backward forcing effect on both industrial structure advancement and scientific and technological innovation, with impact coefficients of 0.0671 and 0.2120, respectively. Compared with scientific and technological innovation, the industrial structure advancement has a greater impact on carbon footprints, with a variance contribution of 25.4%. The research findings are conducive to providing policy support for the coordinated development of BTH and promoting the realization of the Double Carbon goal.