1) Explanation

Let's break down the sentence to understand the context and the meaning required for the blank:
- "Jarring, subversive, and experimental, the films of director Jean-Luc Godard shook the foundation of classical Hollywood style with a thoroughly $\qquad$ approach to cinema."
- The adjectives describing Godard's films are "Jarring, subversive, and experimental." These all imply a departure from the norm, a challenging of established conventions.
- "Shook the foundation of classical Hollywood style" reinforces this idea of breaking away from traditional methods.
- The blank describes the "approach to cinema" that caused this shaking. It needs a word that aligns with "jarring, subversive, and experimental" and contrasts with "classical Hollywood style."

Therefore, the blank needs words that mean groundbreaking, unconventional, or fundamentally new.

Let's evaluate the given options:
- A. revolutionary: Involving or causing a complete or dramatic change. This perfectly aligns with "shook the foundation" and "experimental."
- B. unusual: Not habitually or commonly occurring or done. While Godard's films were unusual, "unusual" is a weaker word than what's implied by "shook the foundation" and "subversive."
- C. conventional: Based on or in accordance with what is generally done or believed. This is the opposite of the implied meaning.
- D. fascinating: Extremely interesting. This describes an effect, not the nature of the approach.
- E. conservative: Holding to traditional attitudes and values and cautious about change or innovation. This is the opposite of the implied meaning.

- F. radical: (Especially of change or action) relating to or affecting the fundamental nature of something; far-reaching or thorough. This is a strong synonym for revolutionary, implying a fundamental and drastic departure from the norm.

Conclusion:

The context strongly suggests an approach that was fundamentally different and transformative, breaking away from established norms. Both "revolutionary" and "radical" convey this meaning effectively.

The final answer is $\(\mathrm{A}, \mathrm{F}\)$.