Crimean–Congo hemorrhagic fever (CCHF) is a viral zoonotic disease resulting in hemorrhagic syndrome in humans. Its causative agent is naturally transmitted by ticks to non-human vertebrate hosts within an enzootic sylvatic cycle. Ticks are considered biological vectors, as well as reservoirs for CCHF virus (CCHFV), as they are able to maintain the virus for several months or even years and to transmit CCHFV to other ticks. Although animals are not symptomatic, some of them can sufficiently replicate the virus, becoming a source of infection for ticks as well as humans through direct contact with contaminated body fluids. The recent emergence of CCHF in Spain indicates that tick–human interaction rates promoting virus transmission are changing and lead to the emergence of CCHF. In other European countries such as France, the presence of one of its main tick vectors and the detection of antibodies targeting CCHFV in animals, at least in Corsica and in the absence of human cases, suggest that CCHFV could be spreading silently. In this review, we study the CCHFV epidemiological cycle as hypothesized in the French local context and select the most likely parameters that may influence virus transmission among tick vectors and non-human vertebrate hosts. For this, a total of 1,035 articles dating from 1957 to 2021 were selected for data extraction. This study made it possible to identify the tick species that seem to be the best candidate vectors of CCHFV in France, but also to highlight the importance of the abundance and composition of local host communities on vectors' infection prevalence. Regarding the presumed transmission cycle involving Hyalomma marginatum, as it might exist in France, at least in Corsica, it is assumed that tick vectors are still weakly infected and the probability of disease emergence in humans remains low. The likelihood of factors that may modify this equilibrium is discussed.