The identification of the protein fold class is a challenging problem in structural biology. Recent computational methods for fold prediction leverage deep learning techniques to extract protein fold-representative embeddings mainly using evolutionary information in the form of multiple sequence alignment (MSA) as input source. In contrast, protein language models (LM) have reshaped the field thanks to their ability to learn efficient protein representations (protein-LM embeddings) from purely sequential information in a self-supervised manner. In this paper, we analyze a framework for protein fold prediction using pre-trained protein-LM embeddings as input to several fine-tuning neural network models, which are supervisedly trained with fold labels. In particular, we compare the performance of six protein-LM embeddings: the long short-term memory-based UniRep and SeqVec, and the transformer-based ESM-1b, ESM-MSA, ProtBERT and ProtT5; as well as three neural networks: Multi-Layer Perceptron, ResCNN-BGRU (RBG) and Light-Attention (LAT). We separately evaluated the pairwise fold recognition (PFR) and direct fold classification (DFC) tasks on well-known benchmark datasets. The results indicate that the combination of transformer-based embeddings, particularly those obtained at amino acid level, with the RBG and LAT fine-tuning models performs remarkably well in both tasks. To further increase prediction accuracy, we propose several ensemble strategies for PFR and DFC, which provide a significant performance boost over the current state-of-the-art results. All this suggests that moving from traditional protein representations to protein-LM embeddings is a very promising approach to protein fold-related tasks.