MOTIVATION: Ancient DNA (aDNA) sequences present unique challenges for taxonomic classification due to extreme fragmentation (reads 20-100 bp), end-biased cytosine deamination, and high contamination rates. Conventional metagenomic classifiers based on exact k-mer matching or alignment lose discriminative power on such short and damaged reads, limiting the analysis of paleogenomic samples. RESULTS: We present FALCON2, a compression-based metagenomic classifier that leverages position-aware finite-context models to maintain high accuracy on degraded viral ancient viruses. FALCON2 consolidates the capabilities of its predecessor, FALCON-meta, into a unified executable with enhanced features including model persistence, direct processing of compressed inputs, multiple file handling, and optional pre-filtering methodologies for contaminated samples. Under controlled benchmarking with database, taxonomy, and thread parity on simulated viral datasets, FALCON2 achieved an Area Under the Curve of Receiver Operating Characteristic (AUC-ROC) of 0.999, an Area Under Precision-Recall Curve (AUPRC) of 0.968, and an F1-score of 0.918, substantially outperforming Centrifuge (AUPRC = 0.625), Kraken2 (AUPRC = 0.184), and CLARK-S (AUPRC = 0.013) on pooled micro-averaged metrics. FALCON2's advantage is most pronounced on ultra-short reads (20-40 bp), where exact k-mers become sparse. FALCON2 pre-filtering at threshold 0.7 improved precision by 10 percentage points with negligible recall loss. FALCON2 runs on systems with 4-8 GB RAM for typical analyses. AVAILABILITY AND IMPLEMENTATION: FALCON2 is freely available at https://github.com/cobilab/FALCON2 under GPL v3 license. Benchmarking data and scripts are archived at DOI: https://doi.org/10.5281/zenodo.17291214.