Despite the advancements in quantum convolution or quanvolution, challenges persist in making quanvolution scalable, efficient, and applicable to multi-dimensional data. Existing quanvolutional networks heavily rely on classical layers, with minimal quantum involvement due to inherent limitations in current quanvolution algorithms. Moreover, the application of quanvolution in the domain of 1D data remains largely unexplored. To address these limitations, we propose a new quanvolution algorithm-Quanv1D-capable of processing arbitrary-channel 1D data, handling variable kernel sizes, and generating a customizable number of feature maps, along with a classification network-fully quanvolutional network (FQN)-built solely using Quanv1D layers. Quanv1D is inspired by the classical Conv1D and stands out from the quanvolution literature by being fully trainable, modular, and freely scalable with a self-regularizing feature. To evaluate FQN, we tested it on 20 UEA and UCR time series datasets, both univariate and multivariate, and benchmarked its performance against state-of-the-art convolutional models (both quantum and classical). We found FQN to outperform all compared models in terms of average accuracy while using significantly fewer parameters. Additionally, to assess the viability of FQN on real hardware, we conducted a shot-based analysis across all the datasets to simulate statistical quantum noise and found our model robust and equally efficient.