Large language models (LLMs) have received considerable interest recently due to their outstanding reasoning and comprehension capabilities. This work explores applying LLMs to vehicular networks, aiming to jointly optimize vehicleto-infrastructure (V2I) communications and autonomous driving (AD) policies. We deploy LLMs for AD decision-making to maximize traffic flow and avoid collisions for road safety, and a double deep Q-learning algorithm (DDQN) is used for V2I optimization to maximize the received data rate and reduce frequent handovers. In particular, for LLM-enabled AD, we employ the Euclidean distance to identify previously explored AD experiences, and then LLMs can learn from past good and bad decisions for further improvement. Then, LLM-based AD decisions will become part of states in V2I problems, and DDQN will optimize the V2I decisions accordingly. After that, the AD and V2I decisions are iteratively optimized until convergence. Such an iterative optimization approach can better explore the interactions between LLMs and conventional reinforcement learning techniques, revealing the potential of using LLMs for network optimization and management. Finally, the simulations demonstrate that our proposed hybrid LLM-DDQN approach outperforms the conventional DDQN algorithm, showing faster convergence and higher average rewards.