Is there any alternative available (apart from high speed train) in regional trains to travel from Toulouse (France) to Madrid (Spain).

For a few reasons:

1. There are currently no connecting trains between Hendaye (France) and Irún (Spain), although they're only a few km apart.
2. Spanish railways only send some of their timetables to the European Timetable Centre, where everybody else get their timetable data from.
3. Spanish domestic reservations cannot be booked through Eurail.
4. There is also a local narrow gauge line from Hendaye via Irún to San Sebastian (Euskotren), but the timetable is only on their own website.
5. Possibly, you're looking too far into the future. On 12 June, there's a small timetable change and the summer timetable in France has not been completely published yet.

Look for a train to Hendaye. If it's a TER train, no reservation is needed.

Then look on the Euskotren website for the timetable from Hendaye (Hendaia) to San Sebastian (Donostia). They run every 30 minutes, are not included in Eurail but are fairly cheap. There are ticket machines in the SNCF Hendaye station (in the main hall, on the right side before the exit) and at the Euskotren station, which is in front of the SNCF station.

Normally, you can get from Pau to Bedous by train and then there are a few buses per day to Canfranc, from where there are 2 trains/day to Jaca and further, see RENFE website. None of these require a reservation (not possible even). You may have to say to the bus driver to Canfranc that you have an SNCF ticket, since they seldomly see rail passes and may not be very familiar with them.

Currently (until 1 May), however, there seem to be engineering works between Oloron and Bedous, where trains are replaced by buses.

Latour-de-Carol - Puigcerdà - Ribes de Freser (- Barcelona) is an extension of the suburban trains of Barcelona. No reservation required (and not possible). You can find the timetable here, where Latour-de-Carol is called "La Tor de Querol”, which is its Spanish name.

Hi @Megb Bhatt I can answer a couple of your questions:
 

1. The reason you can’t book a train from Hendaye (the station on the French side of the border near Biarritz) to San Sebastian is that the section between Hendaye and Irun is only operated by Euskotren, which is not on Interrail. There are two alternatives: i) take the Euskotren train to Irun or San Sebastian - they’re every half hour and it costs about €3.50 I think; or ii) walk (2 km) or take a bus to the RENFE station in Irun. RENFE is on Interrail. I recently walked between the two and the woman in the RENFE station gave me a platform ticket to get onto the local train to San Sebastian, where the booking office was able to reserve my seats to Salamanca (and you can reserve to Madrid).
2. Canfranc is in Spain. There’s a train from Oloron-St. Marie to Bedous, but the old line to Urdos and then in the tunnel under the mountains has not reopened yet. This is forecast to happen in 2025 and then there will be a new train connection between France and Spain. In the meantime there’s a bus several times a day between Canfranc and Bedous - it takes 40 minutes. See https://www.citrampyrenees.fr/ for details. Then you can take a train from Canfranc to Jaca.

On the side: Íe done the Canfranc-Oloron (then before the extension) on a FR TER bus and driver was very familair with InterRail etc. And even if not: local tix now cost 2,30, many regional even very long buslines in this region are very cheap or even free-some FRench socialist policy.