Retrieve a number in a webpage and store in a SQLite3 db
Code smells


your code is vulnerable to SQL injection attacks because you are using string formatting to put query parameters into a query. You need to proper parameterize your query with the help of the database driver:

query = """
    INSERT INTO {table} (datetime, nb_co)
    VALUES(?, ?)
""".format(table=self.forum)
c.execute(query, (now, nb_co))


Note that this way you also don't need to worry about Python to database type conversions and quotes inside parameters - it will all be handled by the database driver.


Performance


instead of re-connecting to the database multiple times, think about connecting to a database once, processing all the data and then closing the connection afterwards
same idea about the use of requests - you may initialize a Session() and reuse
use lxml instead of html.parser as an underlying parser used by BeautifulSoup
you can use SoupStrainer class to parse only the desired element, which will allow you to then simply get the text and split by space instead of applying a regular expression:

parse_only = SoupStrainer(class_="nb-connect-fofo")
page = BeautifulSoup(page_html, 'lxml', parse_only=parse_only)
return page.get_text().split()[0]