Traditional machine learning and deep learning models have demonstrated remarkable performance across various NLP tasks in multiple languages. However, these conventional models often struggle with languages with complex linguistic structures and nuanced contexts, such as Bengali. Recent advancements in quantum computing offer promising solutions for tackling complex, computationally challenging problems, providing faster, more efficient processing than classical systems. This research aims to address the challenges posed by the intricate linguistic structure of the less-resourced Bengali language by developing a quantum-enhanced framework for sentiment classification and claim-checkworthiness identification. We created a classical LSTM framework and proposed novel 2-qubit and 4-qubit classical-quantum frameworks, evaluating their effectiveness for sentiment classification and claim-checkworthiness identification tasks in Bengali. An entirely new dataset comprising ≈3K samples was developed by curating Bengali news headlines from prominent sources. We tagged these headlines with sentiment and claim checkworthy labels using state-of-the-art LLMs. Our findings indicate that the quantum-enhanced frameworks outperform the traditional models in both tasks. Notably, the 4-qubit-based framework achieved the highest F1-score in sentiment classification, while the 2-qubit-based framework demonstrated the best F1-score in claim checkworthiness identification.