I assume your in North America and your car has orange marker lamps at the front?
What you describe sounds like the front turn signal bulbs are being grounded via the marker/tail lamp circuit. When you switch the marker/tail lamps on the turn signal bulb's path to ground is broken causing the turn signal lamps to fail. So, basically you have a poor ground to both front turn signal lamps.
Thanks for the replies. I took the headlights out and ground the bulbs had been twisted in to far causing bad a connection on both. I took them out and reseated them and everything worked as normal. So glad I didn’t have to sort out a bad ground.