Motivated by empirical evidence I document on local credit markets in France using data on more than 3.5 million bank-firm relationships, I propose a theory of bank-firm matching, subject to search frictions. Firms undergo a costly search process to locate and match with the right banking partner. Upon matching, agency frictions hinder bank's ability to optimally screen and monitor projects. I estimate structurally my model on French data using the staggered roll-out of Broadband Internet, from 1997 to 2007, as a shock to search frictions. I confirm the model predictions that a reduction in search frictions affects the allocation of credit and the dynamics of firm-bank matching. Finally, I use the structure of my model to quantify the impact of this technology-induced reduction in search frictions on loan prices. I find that broadband internet access reduced the cost of debt for small businesses by 4.9%