Shalom would be allowed a Goy who is going by car to the same place or place near a Jew (like a synagogue), give a ride to a Jew in Shabbes without the without the Jew to have prompted ? Could the Jew get into the car and go?
You should politely decline the ride.
Here are the halachic problems with taking the ride. The gentile stopped the car and will start again special for you which does involve melacha. The halacha is that we may not benefit from melacha that a gentile does for a Jew, lest we come to ask the gentile to do the melacha for us. Secondly, when you open the door of the car, you will be turning on the interior lights or any sensors that get activated when the door is opened. The same will apply when you close the door. Additionally, being in the gentile’s car on Shabbos while he is driving is zilzul Shabbos.
Therefore, although you technically didn’t ask him for the ride, you should not accept the offer… and you’ll get more schar for walking to shul!
Have a good Shabbos