I'm looking to find a nice running route in the middle of Paris.  I'd
like to start at one particular intersection (rue St. Jacques and rue
Gay-Lussac in the 5th arrondisement).  The run needs to be about 13 km
long (a little less than 8 miles) and stay within the périphérique of
the city (as in, not outside the main highway encircling Paris).

From rue St-Jacque, go down to the seine, run on the quay, cross the
pond to Notre-Dame, cross the park in front of Notre-Dame, Cross the
bridge to Ile St-Louis, Cross completely Ile St-Louis and cross the
last pond, go to Bastille,
and then here you are for 10 more miles on the Coulée -Verte:
http://www.promenade-plantee.org/plan1.html