What's the cheapest way to travel from Paris to Madrid by train?

I am planning to travel from Northern Germany to Madrid by train in March.
I found an offer for a night train to Paris for 43 Euro which is pretty cheap.
From Paris to Madrid, my local train station quoted a price of 173 Euro (incl. bed).
In Germany there are passes for unlimited travel for one day on regional trains for 44 Euros.
Do similar deals exist in France and/or Spain?
I don't care how long it takes or how often I have to change. Also I don't consider the costs of any required overnight stays to be part of the costs. I can justify these as different costs visiting a city.
I do prefer to travel during day time.
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How much is a train ride from Paris to Madrid?
Paris to Madrid by trainJourney timeFrom 10h 45mPriceFrom $48.76Distance654 miles (1052 km)Frequency4 trains per dayFirst train10:105 more rowsIs there a direct train from Paris to Madrid?
Overview: Train from Paris to MadridNormally, there is 1 train operating per day, including direct services available. Travelers depart most frequently from Paris Gare de Lyon and arrive in Madrid-Puerta de Atocha.How long is the train journey from Paris to Madrid?
Paris to Madrid by trainJourney timeFrom 10h 45mDistance654 miles (1052 km)Frequency4 trains per dayFirst train10:10Last train21:455 more rowsDoes the Eurostar go to Spain?
It is possible to travel by train to Spain in a day from the UK. The fastest route is to take the Eurostar from London St Pancras International Railway Station then change in Paris to catch a high speed train to Figueres, Girona and Barcelona.Rnbstylerz \u0026 AREES - WHAT
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