France’s Orange SA does not plan to work with Huawei Technologies Co. to build its fifth-generation mobile network, the first major European phone company to publicly rule out using the Chinese company’s equipment over growing security concerns.

Western governments are worried that Huawei’s systems could be used by Chinese intelligence. Carriers in Australia and New Zealand have been forced to exclude it from their planned 5G networks and the head of British spy agency MI6 said last week the government...