In the field of in situ measurement of high-temperature pressure, fiber-optic Fabry–Perot pressure sensors have been extensively studied and applied in recent years thanks to their compact size and excellent anti-interference and anti-shock capabilities. However, such sensors have high technological difficulty, limited pressure measurement range, and low sensitivity. This paper proposes a fiber-optic Fabry–Perot pressure sensor based on a membrane-hole-base structure. The sensitive core was fabricated by laser cutting technology and direct bonding technology of three-layer sapphire and develops a supporting large-cavity-length demodulation algorithm for the sensor’s Fabry–Perot cavity. The sensor exhibits enhanced sensitivity, a simplified structure, convenient preparation procedures, as well as improved pressure resistance and anti-harsh environment capabilities, and has large-range pressure sensing capability of 0–10 MPa in the temperature range of 20–370 °C. The sensor sensitivity is 918.9 nm/MPa, the temperature coefficient is 0.0695 nm/(MPa∙°C), and the error over the full temperature range is better than 2.312%.