In this paper, we investigate the following fractional nonlinear Choquard equation: \(\begin{aligned} \left\{ \begin{array}{ll} {{\,\mathrm{\varepsilon }\,}}^{2s} (-\Delta )^{s} v +V(x) v= {{\,\mathrm{\varepsilon }\,}}^{-\alpha } (I_{\alpha }*F(v)) F'(v) \text{ in } \mathbb {R}^{N},\\ v\in H^{s}(\mathbb {R}^{N}), \,\, v>0 \text{ in } \mathbb {R}^{N}, \end{array} \right. \end{aligned}\) where \({{\,\mathrm{\varepsilon }\,}}>0\) is a small parameter, \(s\in (0, 1)\) , \(N\ge 2\) , \((-\Delta )^{s}\) denotes the fractional Laplacian, and \(I_{\alpha }\) is the Riesz potential of order \(\alpha \in ((N-4s)_{+}, N)\) . The potential \(V\in C^{0}(\mathbb {R}^N, (0, +\infty ))\) satisfies \(\begin{aligned} m_{0}:=\inf _{\Omega }V<\min _{\partial \Omega }V, \end{aligned}\) for some bounded open set \(\Omega \subset \mathbb {R}^N\) . The function \(F\in C^{1}(\mathbb {R})\) is a nonlinearity of Berestycki–Lions type. By employing suitable variational methods, we establish the existence of at least \(\textrm{cupl}(K)+1\) solutions concentrating around the set \(K:=\{x\in \Omega : V(x)=m_{0} \}\) as \({{\,\mathrm{\varepsilon }\,}}\rightarrow 0^{+}.\)