I come across your question "can I jog with my Papillon" many times and here is my answer:
Look at yourself, and believe , the same rules apply to your dog.
Are you fit?
Are you overweight?
What is your age in relation to the out-put?
Do you run slow?
Marathons, or just a couple of miles?
Do you train frequently, or are you weekend warrior? (which is the most accident prone kind)
The only difference is that your dog has to first learn to be lead on a leash by you, most likely on your left side of your body.
You have to train him just like you did, or do: by going a little at a time, and lead up to longer stretches.
Give your Papi a good health check, make sure he likes that kind of a thing.If his tongue hangs way out, and he is panting a lot after a 1/2 mile or so, bring him back home.
There are many Papis out there who can out run you, but not every Papillon....just like people.
Look at the left column on this blog, there is a link to a nice article on that subject.
And read my article about "Big Dogs, vs Small Dogs" , here on this blog.