The present study investigated the strain response of a distributed optical fiber sensor (DOFS) sealed in a groove at the surface of a concrete structure using a polymer adhesive and aimed to identify optimal conditions for crack monitoring. A finite element model (FEM) was first proposed to describe the strain transfer process between the host structure and the DOFS core, highlighting the influence of the adhesive stiffness. In a second part, mechanical tests were conducted on concrete specimens instrumented with DOFS bonded/sealed using several adhesives exhibiting a broad stiffness range. Distributed strain profiles were then collected with an interrogation unit based on Rayleigh backscattering. These experiments showed that strain measurements provided by DOFS were consistent with those from conventional sensors and confirmed that bonding DOFS to the concrete structure using soft adhesives allowed to mitigate the amplitude of local strain peaks induced by crack openings, which may prevent the sensor from early breakage. Finally, the FEM was generalized to describe the strain response of bonded DOFS in the presence of crack and an analytical expression relating DOFS peak strain to the crack opening was proposed, which is valid in the domain of elastic behavior of materials and interfaces.