Around thirty aristocrats will have their titles abolished by the Spanish Cortes if and when it adopts the Democratic Memory Law (Ley de Memoria Democrática). The text of the law was published in September 2020. At the time, Deputy Prime Minister Carmen Calvo noted that the bill's sixty-six articles would honour the victims of the Franco dictatorship, while reaffirming the importance of democracy and ensuring reconciliation amongst Spaniards.
Here is the full text of the Ley de Memoria Democrática: https://www.mpr.gob.es/servicios/participacion/Documents/APL%20Memoria%20Democrática.pdf
Article 42 of the proposed bill reads:
"Artículo 42. Supresión de títulos nobiliarios.
1. La persona titular del ministerio competente en la gestión de los asuntos relativos a los títulos nobiliarios y grandezas de España elaborará un catálogo de títulos nobiliarios concedidos entre 1948 y 1978, que representen la exaltación de la Guerra y Dictadura, y se procederá a su supresión.
2. Queda suprimida la Orden Imperial del Yugo y las Flechas."
This clearly indicates that the only noble titles which will be affected by this bill are those given to close associates of the Franco dictatorship. As it turns out, there are only thirty-three titles which are actually likely to be abolished. The following list was compiled by El Debate:
1. Duque de Primo de Rivera, con Grandeza de España.
2. Duque de Calvo Sotelo, con Grandeza de España.
3. Duque de Mola, con Grandeza de España.
4. Conde del Alcázar de Toledo, con Grandeza de España.
5. Conde de Labajos.
6. Marqués de Dávila y la Grandeza de España que se le une.
7. Marqués de Saliquet.
8. Marqués de Queipo de Llano.
9. Marqués de Alborán.
10. Conde del Jarama.
11. Marqués de Varela de San Fernando.
12. Conde de Benjumea.
13. Marqués de Somosierra.
14. Grandeza de España otorgada al Conde de Rodezno.
15. Marqués de San Leonardo de Yagüe.
16. Conde de la Cierva.
17. Marqués de Vigón.
18. Conde de Fenosa.
19. Conde del Castillo de la Mota.
20. Marqués de Suanzes.
21. Marqués de Kindelán.
22. Conde de Pallasar.
23. Marqués de Casa Cervera.
24. Conde de Martín Moreno.
25. Marqués de Bilbao Eguía.
26. Grandeza de España a Don Fernando Suárez de Tangil y de Angulo.
27. Conde de Bau.
28. Duque de Carrero Blanco, con Grandeza de España.
29. Señorío de Meirás, con Grandeza España.
30. Duque de Franco, con Grandeza de España.
31. Marqués de Arias Navarro, con Grandeza de España.
32. Conde de Rodríguez de Valcárcel.
33. Conde de lturmendi.
The most prominent title which is likely to cease to exist is the Duchy of Franco (with Grandee of Spain), which was granted to Doña María del Carmen Franco y Polo (1926-2017) by then Prince Juan Carlos of Spain on 26 November 1975, six days after the death of Carmen's father General Francisco Franco.
See here for the official bulletin concerning the granting of the Ducado de Franco: https://www.boe.es/boe/dias/1975/11/27/pdfs/A24781-24781.pdf
The current holder is Doña María del Carmen Martínez-Bordiú y Franco (b.1951), 2nd Duchess of Franco. Carmen's eldest child and only surviving son is Don Luis Alfonso de Borbón y Martínez-Bordiú (b.1974; a pretender to the French throne; uses the title Duke of Anjou in that vein). If and when the law passes, Carmen, who now lives quietly in Portugal, will cease to be the Duchess of Franco, and the title will cease to exist forever. This will likely be a disappointment for her son Luis Alfonso, who would have been his mother's heir to the duchy.
The only other title linked to the Franco family itself that will be abolished is the Señorío de Meirás. This title is currently held by Carmen's brother Don Francisco "Francis" Franco y Martínez-Bordíu (b.1954). However, even if Francis is deprived of the lordship of Meirás, he will still retain the title of Marqués de Villaverde, which he inherited from his father, Don Cristóbal Martínez-Bordiú y Ortega.
For more on the Franco family's situation, there is this article: El ducado de Franco en entredicho: por qué Carmen Martínez-Bordiú no podrá hacer duquesa a su nieta, Eugenia de Borbón
When and if the above thirty-three noble titles are abolished, their former holders will only have recourse by going before the Tribunal Constitucional. This would be a rather difficult course of actions, as the former holders of the abolished titles will have to make the case as to why the original grantee was not associated with the Francoist regime.