Mind you, he was from Basel, a Bernoulli friend, we'd need to investigate first, to determine how he'd likely pronounce his own name!
en.wikipedia.org
And let's not rely only on today's renditions: Strasburg people have always pronounced Broglie as it's written (in French pronunciation), more or less bro' - glee (with a contemporary French r), instead of how the surname Broglie ought to be pronounced: Breuil; Br with a French r, u like in put, y. So, a main place in Strasbourg being Place Broglie (and its unmissable bookstore Librairie Broglie) it is traditionally pronounced Place Bro' - glee. It's the proper pronunciation of the place, diverging from the proper pronunciation of the surname for historical reasons. It's now been 15-20 years that Strasbourg people have started to pronounce Br - u -y as in the surname Broglie! Even the tramway announcements are this way! It cringes! In the same way, Basel people may have changed their pronunciation of Euler, for instance under "foreign" influence. This will make our investigation all the more difficult.