import re

pattern = r"\bJane(?:'?s|\(s\))? car\b|\b(car)\b"

s = ("for example\n"
            "    the car is red  - Match\n"
            "    here is Jane car is red  -> None\n"
            "    here is Janes car is red  -> None\n"
            "    here is Jane's car is red  -> None\n\n"
            "2. I also want to find the cases Jane is in the phrase\n"
            "    the car is red  - None\n"
            "    here is Jane car is red  - Match\n"
            "    here is Janes car is red  - Match\n"
            "    here is Jane's car is red  - Match\n\n"
            "3.  and where car is not preceding by Jane(s)\n"
            "    here Jane(s) car is red  - None\n\n"
            "4. and of course the opposite\n"
            "   here is Jane(s) car is red  - Match")
result = [m for m in re.findall(pattern, s) if m]
print(result)