Understanding public sentiment on climate change and environmental issues is essential for evaluating public awareness, gauging policy support, and identifying the spread of misinformation. This study analyzes sentiment trends in online discussions related to climate change by leveraging social media data from platforms such as Twitter and Reddit. We propose a hybrid sentiment analysis framework that integrates lexicon-based techniques with deep learning, specifically by fine-tuning ClimateBERT, to classify posts into positive, negative, and neutral categories. Experimental results demonstrate that the fine-tuned ClimateBERT model achieves an F1-score of 90%, significantly outperforming traditional sentiment analysis techniques, including lexicon-based methods and conventional machine learning classifiers. The comparative analysis underscores the limitations of rule-based sentiment scoring in capturing nuanced sentiment shifts within complex environmental discourse. The findings offer valuable insights into public opinion on climate change, reveal patterns of misinformation and polarization, and carry implications for environmental policy-making, media monitoring, and sustainability advocacy.