I have schengen visa issued by French embassy and my longer stay would also be in the same country. My first stay would also be at Paris. However, as per my flight, I will break the journey at Frankfurt, Germany and have to go for immigration before taking connecting flight to Paris in next two hours. Will it have any problem at immigration at Frankfurt?
Short answer, No.
I did almost the exact same thing in the past. I had a French long stay visa and entered the Schengen Region thru Amsterdam and then traveled to France via Train.
As long as you have a valid Schengen Visa, you should not have a problem at Germany thru immigration. Also, you have a valid connecting flight to Paris in the next few hours so the Visa Official would not be concerned.
Check answers here for more information - Should my first trip be to the country which issued me Schengen Visa?