logger.exception will output a stack trace alongside the error message.

For example:

import logging
try:
    1/0
except ZeroDivisionError:
    logging.exception("message")

Output:

ERROR:root:message
Traceback (most recent call last):
  File "<stdin>", line 2, in <module>
ZeroDivisionError: integer division or modulo by zero

@Paulo Cheque notes, "be aware that in Python 3 you must call the logging.exception method just inside the except part. If you call this method in an arbitrary place you may get a bizarre exception. The docs alert about that."

Current function name, module and line number you can do simply by changing your format string to include them.

logging.basicConfig(
    filename = fileName,
    format = "%(levelname) -10s %(asctime)s %(module)s:%(lineno)s %(funcName)s %(message)s",
    level = logging.DEBUG
)

Most people only want the stack when logging an exception, and the logging module does that automatically if you call logging.exception(). If you really want stack information at other times then you will need to use the traceback module for extract the additional information you need.

You are on the right track. I recommend that you read the logging HOWTO, it explains a lot of things.

You can use levels and filters to decide if your handler should handle or not the log. And you can use a Formatter to add the stacktrace to the log record message.

Here is a Proof-of-Concept :

import logging
import traceback
import sys


logger = logging.getLogger("app.main")


class StacktraceLogFormatter(logging.Formatter):
    def format(self, record: logging.LogRecord) -> str:
        stack_lines = traceback.format_stack()
        # we have the lines down to ^^^^^^ this call, but we don't want to show it, nor the internal logging ones
        stack_lines_without_logging_intermediary_calls = filter(
            lambda line: ("lib/logging/__init__.py" not in line)
                         and ("lib\\logging\\__init__.py") not in line,
            stack_lines[:-1]
        )
        return record.msg + "\nOrigin :\n" + "".join(stack_lines_without_logging_intermediary_calls)
        # beware of : https://stackoverflow.com/q/8162419/11384184


class InfoOrLessFilter(logging.Filter):
    def filter(self, record: logging.LogRecord) -> bool:
        return record.levelno <= logging.INFO


def do_some_logging():
    logger.debug("debug message")
    logger.info("info message")
    logger.warning("warning message")
    logger.error("error message")
    try:
        1/0
    except ZeroDivisionError:
        logger.exception("exception message")
    logger.critical("critical message")


def setup_custom_logging():
    logger.handlers = []  # remove the existing handlers from the logger

    regular_handler_for_info_messages = logging.StreamHandler(sys.stdout)
    regular_handler_for_info_messages.setLevel(logging.DEBUG)  # at least DEBUG
    regular_handler_for_info_messages.addFilter(InfoOrLessFilter())  # but not more than INFO
    logger.addHandler(regular_handler_for_info_messages)

    stacktrace_handler_for_important_messages = logging.StreamHandler(sys.stderr)
    stacktrace_handler_for_important_messages.setLevel(logging.INFO + 1)  # more than INFO
    stacktrace_handler_for_important_messages.setFormatter(StacktraceLogFormatter())
    logger.addHandler(stacktrace_handler_for_important_messages)

    logger.propagate = False


def main():
    logging.basicConfig(level=logging.DEBUG)
    do_some_logging()
    setup_custom_logging()
    do_some_logging()


if __name__ == "__main__":
    main()

It produces before :

debug message
info message
DEBUG:app.main:debug message
INFO:app.main:info message
WARNING:app.main:warning message
ERROR:app.main:error message
ERROR:app.main:exception message
Traceback (most recent call last):
  File "C:/PycharmProjects/stack_overflow/67846424.py", line 43, in do_some_logging
    1/0
ZeroDivisionError: division by zero
CRITICAL:app.main:critical message

and after :

warning message
Origin :
  File "C:/PycharmProjects/stack_overflow/67846424.py", line 73, in <module>
    main()
  File "C:/PycharmProjects/stack_overflow/67846424.py", line 69, in main
    do_some_logging()
  File "C:/PycharmProjects/stack_overflow/67846424.py", line 40, in do_some_logging
    logger.warning("warning message")

error message
Origin :
  File "C:/PycharmProjects/stack_overflow/67846424.py", line 73, in <module>
    main()
  File "C:/PycharmProjects/stack_overflow/67846424.py", line 69, in main
    do_some_logging()
  File "C:/PycharmProjects/stack_overflow/67846424.py", line 41, in do_some_logging
    logger.error("error message")

exception message
Origin :
  File "C:/PycharmProjects/stack_overflow/67846424.py", line 73, in <module>
    main()
  File "C:/PycharmProjects/stack_overflow/67846424.py", line 69, in main
    do_some_logging()
  File "C:/PycharmProjects/stack_overflow/67846424.py", line 45, in do_some_logging
    logger.exception("exception message")

critical message
Origin :
  File "C:/PycharmProjects/stack_overflow/67846424.py", line 73, in <module>
    main()
  File "C:/PycharmProjects/stack_overflow/67846424.py", line 69, in main
    do_some_logging()
  File "C:/PycharmProjects/stack_overflow/67846424.py", line 46, in do_some_logging
    logger.critical("critical message")