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Projects such as the European Covid-19 Forecast Hub publish forecasts on the national level for new deaths, new cases, and hospital admissions, but not direct measurements of hospital strain like critical care bed occupancy at the sub-national level, which is of particular interest to health professionals for planning purposes. We present a sub-national French framework for forecasting hospital strain based on a non-Markovian compartmental model, its associated online visualisation tool and a retrospective evaluation of the real-time forecasts it provided from January to December 2021 by comparing to three baselines derived from standard statistical forecasting methods (a naive model, auto-regression, and an ensemble of exponential smoothing and ARIMA). In terms of median absolute error for forecasting critical care unit occupancy at the two-week horizon, our model only outperformed the naive baseline for 4 out of 14 geographical units and underperformed compared to the ensemble baseline for 5 of them at the 90% confidence level (n = 38). However, for the same level at the 4 week horizon, our model was never statistically outperformed for any unit despite outperforming the baselines 10 times spanning 7 out of 14 geographical units. This implies modest forecasting utility for longer horizons which may justify the application of non-Markovian compartmental models in the context of hospital-strain surveillance for future pandemics. Author summary: The US and European Covid-19 Forecast Hubs focus on metrics such as deaths, new cases, and hospital admissions, but do not offer measurements of hospital strain like critical care bed occupancy, which was essential for the provisioning of healthcare resources during the COVID-19 pandemic. Furthermore, forecasting support was only guaranteed on the national level leaving many countries to look elsewhere for valuable sub-national forecasts. In France statistical modelling approaches were proposed to anticipate hospital stain at the sub-national level but these were limited by a two-week forecast horizon. We present a sub-national French modelling framework and online application for anticipating hospital strain at the four-week horizon that can account for abrupt changes in key epidemiological parameters. It was the only publicly available real-time non-Markovian mechanistic model for the French epidemic when implemented in January 2021 and, to our knowledge, it still was at the time it stopped in early 2022. Further adaptations of this surveillance system can serve as an anticipation tool for hospital strain across sub-national localities to aid in the prevention of short-noticed ward closures and patient transfers. [ABSTRACT FROM AUTHOR]