PARIS (Reuters) - Britain's vote to leave the European Union should bring more investment into France and make the country a gateway to the European market, President Francois Hollande said on Tuesday.

"Britain's decision to leave the European Union should make us seek even more investments, make us showcase France's attractiveness," Hollande told journalists at a FedEx Corp <FDX.N> facility in Paris suburb of Roissy after the package delivery company announced a 1.4 billion-euro investment in France.

"It's not about taking what Britons have, but once they've made this choice, they must live with the consequences and we, France, must become the point of access to the European market," he added.

Since the Brexit vote in June, many EU countries have sought to take advantage of the situation by wooing investors interested in keeping access to the EU's vast single market.

(Reporting by Jean-Baptiste Vey; Writing by Mathieu Rosemain; editing by Michel Rose)