The status of the energy storage is generally ambiguous, either generation, consumption, or both. This study evaluates the largest French Pumped Hydro Storage plant - Grand'maison, by means of an optimization dynamic algorithm of the plant hourly operation over one year. In this market model, the storage operator has perfect information on the spot market price over one day for a daily storage provision; alternatively, it considers a weekly storage strategy, hence with myopic foresights of prices over the year but perfect information within recursive weekly blocks. Results show that the storage operator does not fully capture the market value, and partly confirm expectations that the storage economic model is not driven by the spot price, but it simply correlates with. Despite optimisation, the French price spread is not large enough to cover the investment costs (the NPV before taxes is of -34 M€2017/yr or -23 €2017/MWh). This further supports the design of contractual options for PHS as ancillary services provider and stand-alone market player, or some forms of vertical integration, e.g. with the TSO or with nuclear or renewables generators. These revenue streams seem implicit today to the economics of PHS, and their value alone would justify the French regulator commitment to install new PHS plants despite unclear inhibiting business models.