It is possible to get by without, but on less frequented routes where there is little pilgrim-specific accommodation it is better to have at least basic Spanish.
On the busier routes you will meet various non-French and non-Spanish pilgrims who generally will speak some English, but you should not expect to meet many English-speaking Spaniards, pilgrim or otherwise.
Your enjoyment of France and Spain and the people you meet will be greatly enhanced if you can find the time to learn some basic French or Spanish (hello, goodbye, please, thank you, enough vocabulary to use in shops and restaurants and to ask for a bed or room for the night). We strongly suggest investing in an evening class, or a teach-yourself book/audio course, or trying one of the many free online learning resources, such as http://www.bbc.co.uk/languages/. You may wish consider buying a small lightweight phrasebook too.
We offer the book Camino Lingo in our online shop.
The Instituto Cervantes, 102 Eaton Square, London SW1W 9AN (020 7245 0621) offers Spanish language classes. Their website is londres.cervantes.es/en/default.shtm
Or how about a Spanish language course at the University of Santiago itself? The University also offers Spanish-language courses which include a week on the Camino or Spanish-language courses for hospitaleros.
The City Hall School of Languages in Léon offers a one-week Spanish for Pilgrims course.