The language that is widely spoken in Boquete is of course Spanish because Panama is a Spanish-speaking country. However, because of the large settlement of expats in Boquete, there are a lot of jobs that require Panamanians to learn some English. That has attracted English-speaking Panamanians from other locations to come to Boquete. There is a high concentration of English-speaking Panamanians in service jobs such as hotel clerks, waiters in restaurants, and clerks in the stores.
When you live in Boquete it is better if you learn some rudimentary Spanish. There are two very good Spanish language schools here. You can certainly get by with just basic Spanish. You can survive without it but it does not enhance your life here if you do not know any Spanish at all.