Lodz was a highly industrial city that was only built up starting in the 1820s. The city actively attracted workers from throughout the Russian Empire and Germany as well.
There was a revolution in Russia in 1905 after Russia list the Russo-Japanese war
It led to an opening in government and a parliament
Revolutionary activity - by socialists, communists, and others - surged.
Jews were especially involved.
It could be that your ancestors were involved in this kind of activity in Lodz, organizing, planning.
They would have come under the suspicion of the Czar's police
Exile to Siberia was often the result
It is quite possible this is why they left for France, a common destination for refugee revolutionaries.
San Francisco, CA, USA
Weinstein -> Solotwina, Galicia | Frisch, Hilman, Jungerman, Schindler -> Rozniatow, Galicia | Golanski, Kramerofsky/Kromerovsky -> Kiev | Lefkowitz -> Petrikov, Belarus | Shub, Rosen Hlusk, Belarus | Levine, Weiner, Zamoshkin -> Slutsk, Belarus