There are a number of ways to handle this, depending on how the quotes were keyed in the first place. Also, if there is no usage of paragraph styles, it can be inconvenient to re-mark all of the text as English text. That being said, if you have successfully re-marked all text as English, you should be able to do a Find for a single quote mark, and Replace All with a single quote mark, and all of the quotes should behave as you have assigned them to (e.g. English typographer's quotes).
If you pulled down the lang dropdown and just selected English with the cursor sitting in text, this probably won't work. If styles are used in the template, check there in the Advanced Character Formats for the language setting.
- Your paragraph style has to have the correct language. If it is Germany/Austrian German DE-DE you get normally „…“ or »…«, if it is US-EN you will get “…”
- You have to make the correct settings in InDesign's preferences in the Dictionary section for each language separately.
- If you have changed the language or the settings after importing or writing text, it will not change automatically, but it is easy to perform, find and replace a " with a ", it will change automatically with the correct apostrophe.